A self-excited MEMS electro-quasi-static induction turbine
generator
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Steyn, J.L. et al. “A Self-Excited MEMS Electro-Quasi-Static
Induction Turbine Generator.” Microelectromechanical Systems,
Journal of 18.2 (2009): 424-432. © 2009, IEEE
As Published
http://dx.doi.org/10.1109/JMEMS.2008.2011692
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Institute of Electrical and Electronics Engineers / American
Society of Mechanical Engineers
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424
JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 18, NO. 2, APRIL 2009
A Self-Excited MEMS Electro-Quasi-Static
Induction Turbine Generator
J. Lodewyk Steyn, Sam H. Kendig, Ravi Khanna, Stephen D. Umans, Fellow, IEEE,
Jeffrey H. Lang, Fellow, IEEE, and Carol Livermore
Abstract—This paper presents a microfabricated electro-quasistatic (EQS) induction turbine generator that has generated net
electric power. A maximum power output of 192 μW was achieved
under driven excitation. We believe that this is the first report
of net-electric-power generation by an EQS induction machine of
any scale found in the open literature. This paper also presents
self-excited operation in which the generator resonates with an
inductor and generates power without the use of external activedrive electronics. The generator comprises five silicon layers,
fusion-bonded together at 700 ◦ C. The stator is a platinumelectrode structure formed on a thick (approximately 20 μm)
recessed oxide island. The rotor is a thin film of lightly doped
polysilicon also residing on a 10-μm-thick oxide island. Carrier
depletion in the rotor conductor film limited the performance of
the generator. This paper also presents a generalized state-space
model for an EQS induction machine that takes into account the machine and its external electronics and parasitics.
This model correlates well with measured performance and
was used to find the optimal drive conditions for all driven
experiments.
[2007-0253]
Index Terms—Electro-quasi-static (EQS) induction generator,
electrostatic machine, power MEMS, self-excitation, turbine
generator.
I. I NTRODUCTION
B
ATTERIES have been, and still remain, the energy-storage
medium of choice for many portable electric and electronic applications. Most hydrocarbon fuels have energy denManuscript received October 24, 2007; revised August 26, 2008. Current version published April 1, 2009. The work of J. L. Steyn was supported in part by an Applied Materials Graduate Fellowship. The work of
S. H. Kendig was supported by the Reed Fund. The work at Lincoln Laboratory was supported by the Defense Advanced Research Projects Agency
under Air Force Contract F19628-00-C-0002. Funding for the development
of microengine technology was provided by the Army Research Laboratory
(DAAD19-01-2-0010) under the Collaborative Technology Alliance in Power
and Energy Program, managed by J. Hopkins (ARL) and Dr. M. Acharya
(Honeywell) and by the Army Research Office (DAAG55-98-1-0292) managed
by Dr. T. Doligalski. This work was presented in part at the 18th International
Conference on Micro Electro Mechanical Systems, Miami, FL, January 30–
February 3, 2005. Subject Editor C.-J. Kim.
J. L. Steyn is with Pixtronix Inc., Andover, MA 01810 USA (e-mail:
lodewyk@alum.mit.edu).
S. H. Kendig is with Bose Corporation, Framingham, MA 01701 USA.
R. Khanna is with BAE Systems, Lexington, MA 02421 USA.
S. D. Umans is an independent Consultant residing in Belmont, MA 02178
USA.
J. H. Lang is with the Department of Electrical Engineering and Computer
Science, Massachusetts Institute of Technology, Cambridge, MA 02139-4307
USA.
C. Livermore is with the Department of Mechanical Engineering,
Massachusetts Institute of Technology, Cambridge, MA 02139-4307 USA.
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JMEMS.2008.2011692
sities that are approximately 20–30 times greater than those of
most batteries and, therefore, present an attractive alternative,
provided that a means can be found to convert the enthalpy
of combustion of a hydrocarbon fuel into electric power. On
the macroscale, gas-turbine (Brayton) cycles can have high
efficiencies and coupled turbomachines and electric generators lend themselves to reliable continuous operation for long
periods of time. Such gas turbine generators have been very
successful at the kilowatt level and above.
Research at MIT has focused on the development of a
miniaturized gas turbine generator to deliver 1–50 W of electric
power [1]. In this device, a small gas turbine engine provides the
shaft power needed to drive a small electric generator. Presented
in this paper is an electro-quasi-static (EQS) induction generator for that system. Although magnetic machines are preferred
at large scales, EQS machines become attractive at small scales,
primarily because very small air gaps between the rotor and
stator allow higher electric fields before breakdown, on the order of 108 V/m. Higher electric fields make it possible to build
a high-power-density EQS machine. Macroscale EQS motors
have been reported previously, but even relatively small conventionally fabricated devices (e.g., [2], [3]) perform rather poorly
as compared to their magnetic counterparts. Previously at MIT,
Nagle et al. [4], [5], Fréchette et al. [6], and Livermore et al. [7]
presented microfabricated EQS induction micromotors. The device in [7] attained a maximum speed of 55 krpm, a maximum
torque of 3.5 μN · m, and a maximum air-gap power of 20 mW,
the highest air-gap power of any MEMS electric micromotor.
Attempts to produce an EQS induction generator have, until
now, not been successful [8].
This paper describes the first successful creation and operation of an EQS generator that outputs net electrical power.
The fundamental challenge of EQS generators (as compared
to EQS motors) is their sensitivity to parasitic capacitances
between the point at which power is generated and the point
at which that power is used. If losses caused by the presence
of parasitic capacitance within an EQS generator exceed its
generating capacity, its power output falls to zero. In contrast,
those same losses in an EQS motor would take place before the
point at which power is converted to the mechanical domain.
Thus, they would reduce motoring efficiency but not the ultimate mechanical output power. The generator demonstrated in
this paper is therefore similar but not identical to the motors
described in [6] and [7]. Key differences in the structure and
operational protocol that enable generation in the present device
are presented in this paper along with the power-generation
results that they enable.
1057-7157/$25.00 © 2009 IEEE
STEYN et al.: SELF-EXCITED MEMS ELECTRO-QUASI-STATIC INDUCTION TURBINE GENERATOR
425
Fig. 2. Three-dimensional section view of the turbine-generator device. The
generator stator electrodes are shown arranged like spokes on a wheel. The
connections of three of the six phases to the external bonding pads (stator leads)
are shown.
Fig. 1. Essence of an EQS induction machine. Basic six-phase machine
consists of a stator with a set of electrodes arranged such that every sixth
electrode is connected. Sinusoidal voltages on the six electrode sets, phased
60◦ apart, produce a traveling wave. This in turn induces a traveling potential
wave on the rotor—a high-resistivity polysilicon film in this case.
II. D EVICE L AYOUT AND O PERATION
Fig. 1 shows a description of the essence of the EQS induction machine. The machine comprises a spinning rotor and
a fixed stator that interacts with the rotor. On the surface of
the stator is an array of radial electrodes; every sixth stator
electrode is connected to form one phase in a six-phase machine. The rotor in the present machine is coated with a highresistivity polysilicon film. Sinusoidal voltages on the six
phases, phased 60◦ apart, produce a traveling stator potential
wave. The traveling potential wave on the stator induces a
traveling potential wave on the rotor. If the rotor spins slower
than the stator potential wave, the machine operates as a motor.
If the rotor spins faster, as shown in Fig. 1, it operates as a
generator. Correspondingly, the combination of the rotor film’s
high resistivity and its stray capacitance causes the rotor potential to lag/lead the stator potential during motoring/generating
operation. In the present machine, the backside of the rotor
disk (away from the stator) is occupied by a set of turbine
blades that spin the rotor when they are supplied with pressurized air [1]. During operation, the rotor is supported on air
bearings [9], [10].
The actual device is shown in schematic 3-D cross section
in Fig. 2. The device structure is similar to devices presented
earlier [4], [6], [7]. In Fig. 2, the first layer L1 provides connections for the main air supply of the turbine and for the air supply
to the front thrust bearing. Layer L2 includes the turbine main
air-distribution manifold and the air-injection ports for the front
thrust bearing. The turbine rotor and stator blades are formed
on the topside of L3; the rotor itself and the journal bearing that
supports it in the plane of the wafer are also defined in L3. The
bottom of L3 has the rotor film for the induction machine on
top of a thick (10 μm) oxide island. Layer L4 is the stator, with
786 platinum electrodes arranged in 131 interleaved groups of
six electrodes on top of a thick (approximately 20 μm) oxide
island. L4 also includes the air-injection ports for the rear thrust
bearing. L5 provides air connections for the rear thrust bearing
Fig. 3. Schematic cross-sectional view of a section of the generator, showing
the stator electrodes fabricated on the oxide-coated stator substrate along with
one of the six concentric interconnection rings that groups the electrodes
together into six phases. Also shown is the rotor film on its oxide-coated rotor
substrate. The potentials Vi are indicated on the six stator phases; the phase
interconnection for phase four is shown.
Fig. 4. Photograph of the generator device.
and the journal bearing of the turbine. Fig. 3 shows a schematic
cross section of one section of the rotor/stator structure, and
Fig. 4 shows a photograph of the actual device.
III. F ABRICATION
The generator is fabricated using standard integrated-circuit
fabrication techniques, deep reactive-ion etching (DRIE), and
multiwafer bonding. Its fabrication is similar to that described
in [6] and is identical to that described in [7], except for
the high-speed bearing fabrication and the preparation for and
execution of the full-stack wafer bond, which are described as
follows. Layers L1, L2, and L5 are fabricated primarily through
double-sided DRIE. Layer L4 combines those processes with
the fabrication of the electrical features of the stator; L3 is
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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 18, NO. 2, APRIL 2009
similar but includes the additional challenge of etching the deep
high-aspect-ratio journal-bearing feature as in [11].
A. High-Speed Bearing Fabrication
The journal bearing in L3 is designed to be 20 ± 1 μm wide
and 300 μm deep. The results presented in this paper are from
a device with a 21 ± 1 μm wide and approximately 300-μmdeep bearing. Good control of the journal-bearing fabrication
enables rotational speeds of up to 850 krpm to be reached. The
speed limit is attributed to destabilizing forces resulting from
air-gap nonuniformities caused by deviations from a flat stator
topography.
B. Rotor and Stator Fabrication With Thick
PECVD Oxide Films
Thick silicon-dioxide layers are required in Layers L3 and
L4 to minimize parasitic capacitive coupling to the rotor and
stator backplanes. To minimize wafer bow, the insulator oxide
is limited to buried islands where it is needed as in [12].
The rotor oxide is a 10-μm-thick plasma-enhanced chemicalvapor-deposition (PECVD) film, and the stator oxide is an
approximately 20-μm-thick PECVD tetraethyoxysilane film.
The 0.5-μm-thick polysilicon rotor film is deposited by lowpressure CVD and doped with boron by ion implantation. The
stator fabrication process is described further in [7]. The bond
between L3 and L4 is a fusion bond between PECVD oxide
and silicon. The PECVD oxide is smoothed by repeated oxide
deposition and chemical–mechanical polishing until a bondable
surface is obtained as demonstrated by successful contacting to
a test wafer. After smoothing, L4 is annealed at 750 ◦ C for 3 h
to outgas the PECVD oxide, while ensuring that the platinumstator-electrode structure does not develop hillocks. Only then
does the fabrication of L4 proceed to the etching of the throughwafer flow paths and to bonding. The bondability-verification
procedure with known good blank wafers, combined with
rework where needed, enables the bonding of the five-layer
wafer stack with 100% bond yield. The final room-temperaturebonded stack is room-temperature pressed with a uniform load
of 3 kN for 24 h, then placed under a uniform thermal press of
3 kN for 4 h at 500 ◦ C, and finally, annealed at 700 ◦ C for 22.5 h.
IV. C ONCEPTS FOR S YSTEM A RCHITECTURE ,
M ODELING , AND O PERATION
When the rotor of the EQS device spins faster than the
traveling speed of the stator’s potential wave, power is transferred from the rotor to the stator. However, if the power lost
in the rest of the generator system (including its parasitics
and external electronics) exceeds the power sourced by the
rotor–stator interaction, the generator system as a whole will
fail to generate net power. Therefore, to demonstrate a complete
generator system, one must first choose the system’s mode
of operation, design the external electronics that enable that
operation, and model the complete system in detail to ensure
that it can be tuned to operate as intended.
Two different system architectures and modes of operation
were used in the course of the experiments described here.
Fig. 5.
strays.
Machine model that includes the resonant electronics and the external
The two operational modes have related (but not identical)
challenges and require related (but not identical) models to
understand and address those challenges.
In the first operating mode, the six generating phases of the
machine were each driven externally at a common frequency
but with phase-specific driving voltages and phase shifts.
Driven excitation could be implemented by driving each of the
generator phases directly with electronics based on MOSFET
inverters, but the power consumption of the external electronics
would exceed the power produced by the EQS generator and
prevent net generation of electric power. Instead, electronics
were created to drive the generator phases through a combination of low-level drive voltages and resonant circuits to amplify
the voltages onto the generator phases. A single phase of the
EQS machine, its parasitics, and the resonant external electronics are shown in Fig. 5. The inductor resonates at the design
electrical frequency with the combined machine capacitance
and external stray capacitance, and RSi represents the load. The
parasitics shown in Fig. 5 are described further in Section V.
The second operating mode employed a self-excited
architecture. The electronics for this approach are similar to
those shown in Fig. 5, except that the driving voltages VDi
are each replaced by a connection to ground. The resonant
circuits formed by the generator, the stray capacitance, and the
inductors self-excite the phase voltages by amplifying small
fluctuations. As long as the rotor speed is set to an appropriate
value above the speed of the stator’s traveling wave and the
stator’s parasitics are sufficiently small and well balanced, the
resonance automatically selects the optimal phase voltages,
phase shifts, and electrical frequency.
Both driven- and self-excitation require that the parasitic
capacitance and the wiring resistance be minimized to reduce
ohmic losses. Both operating modes also require that the imbalance among the generator phases be minimized, so that the
capacitance of each generator phase to ground and to the other
generator phases is as uniform as possible. Finally, each mode
requires that some set of electronic parameters be optimized in
order to ensure that net power is generated. These requirements
were met through a combination of the following features:
1) complete system modeling; 2) careful design and layout of
the external electronics; and 3) detailed parameter estimation
to ensure the accuracy of the models. The externally driven
approach requires a steady-state sinusoidal model that predicts
power output; parameters can be chosen by optimizing for
maximum power output. The self-excited approach requires an
eigenvalue analysis; parameters can be chosen by maximizing
STEYN et al.: SELF-EXCITED MEMS ELECTRO-QUASI-STATIC INDUCTION TURBINE GENERATOR
427
the real part of the eigenvalues. A detailed state-space model
was used to meet the requirements of both sets of experiments;
for the experiments under driven excitation, the system
was analyzed with sinusoidal driving voltages. The model
is described in Section V. Detailed parameter-estimation
experiments were performed to determine the values of the
internal and external stray capacitances and also to characterize
the external inductors. These experiments are described in
Section VI. The driven and self-excited experiments are
described in Sections VII and VIII, respectively.
(RL ), and wire-insulation-dielectric (RC ) losses. This model
accurately and successfully guided the experiments discussed
in this paper and helped to determine the optimal drive voltages
and phase angles VDi , i ∈ {1, 2, 3, 4, 5, 6}, whenever a driven
excitation was used.
Combining the lumped-parameter representation of the fields
with the model representation of the strays yields a state-space
model of the form
V. D EVICE M ODELING
In (1), the state vector X is comprised as [V p ψ0 ξ w VC iL ]T .
The entries in the state matrices A, B, and C are obtained
from the Fourier decomposition of the fields problem; they are
given with derivation in [15]. VD is the drive-voltage vector.
The rotor potential p has dimension 2n × 1, where n is the
number of harmonics used to approximate the stator wave; we
need twice the number of harmonics to account for the sine and
cosine terms or, equivalently, the amplitude and spatial phase of
each harmonic. We used 13 harmonics for all subsequent modeling of the generator, and therefore, p has dimension 26 × 1.
The vector V represents the potentials on the six statorelectrode sets. ψ0 and ξ are scalars and represent the zeroth
harmonic of the rotor conductor potential and the potential of
the rotor backside. VC and iL are a potential in and the current
through the inductor, respectively, as shown in Fig. 5. With V,
w, VC , and iL all being of dimension 6 × 1 and p being
of dimension 26 × 1, (1) represents a 52-state system. The
machine casing is assumed to be at zero potential.
The concepts described in Section IV are implemented in a
state-space model of the EQS machine. This model improves
on the work by Nagel [4] and Bart and Lang [13] that addressed mainly the rotor- and stator-field analyses and assumed
balanced operation in which all the phases of the electric
machine can be treated as being identical. The model presented
here treats each of the six machine phases as unique and also
accounts for unique coupling between the various phases.
The first step in developing the machine model is to represent the fields within the rotor–stator structure in a lumpedparameter form. The field and circuit theories developed in this
paper then feeds into the state-space model. We use the same
starting point that was used in [4] and [13] and approximate the
polar machine, shown in Fig. 1, as a wrapped linear induction
machine. The Cartesian representation of the wrapped linear
induction machine is shown in Fig. 3, where φ(t) represents
the potential on the stator and ψ(t) represents the potential
on the rotor. The turbine disk is assumed to be grounded
through a capacitor CB . A Fourier decomposition of the stator
potential, in turn, provides a Fourier representation of the rotor
potential and the air-gap electric fields as well as the fields
in the rotor and stator half-spaces. Once the fields on both
sides of the stator electrodes are obtained, one can use Gauss’s
law to solve for the charge on the stator electrodes, thereby
obtaining a current–voltage relationship for the machine in
lumped-parameter format.
The next step is to add the relevant internal and external
parasitic stray components, as shown in Fig. 5. The model
includes the inductors that make this a resonant system and the
coupling to the other phases. In Fig. 5, CSij are components
of the general nonsymmetric stator capacitance matrix and
include contributions from the six stator interconnect rings, the
six stator leads, and the six bond pads. The subscripts i and
j refer to phases one through six. The contributions of the
interconnect rings toward CSij were obtained by simulating a
portion of the stator structure in FastCap, a boundary-elementmethod capacitance solver [14]. The contributions of the stator
leads were computed using parallel-plate theory. Rmi are the
combined resistances of the leads, interconnect wiring, vias,
and electrodes of the stator itself. CEij are components of the
general nonsymmetric external stray-capacitance matrix. CEij
were modeled using FastCap. To obtain an accurate model,
it was necessary to reestimate this matrix using experimental
techniques. Each of the six inductors attached to the machine
was independently modeled to include core (RLp ), wiring
AẊ = BX + CVD .
(1)
VI. C HARACTERIZATION AND P ARAMETER E STIMATION
To excite the six-phase generator, six voltage amplitudes (VDi
in Fig. 5), five phases shifts, the frequency, and the speed must
all be specified. The generated power will depend on all 13 of
these parameters. Finding the optimal operating point experimentally is impractical, so a model-guided computer-optimized
approach is preferred. This requires an accurate model. Therefore, the model described in Section V must be calibrated to the
actual machine and its experimental setup. The machine was
characterized using a frequency-domain method. The generator
was spun at 50 krpm. Each phase (VDi ) of the machine was in
turn swept in frequency while the other phases were grounded.
The resulting voltages wi (magnitude and phase) were recorded
for all six phases. This experiment was repeated six times to
give six data sets, each with a magnitude and phase response for
all six phases, and therefore, 36 frequency-response functions
(FRFs). The model was then compared to the experimental
data, and a nonlinear least squares algorithm was used to adjust
the external capacitance matrix CEij , the gap G, and the rotor
conductivity σs to best fit the data. Fig. 6 shows a description
of this parameter-estimation procedure. Fig. 7 shows the FRF
for the case in which Phase 1 was the driven phase and all
the others were grounded, together with the model result after
fitting. Typical values for CEij , i = j and CEij , i = j were 4.5
and 0.5 pF, respectively. For the gap and the rotor conductivity,
values of G = 4.2 μm and σs = 0.75 nS were obtained.
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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 18, NO. 2, APRIL 2009
Fig. 6. Parameter-estimation flow diagram.
Fig. 8. Individual per phase powers versus mechanical speed. Negative power
indicates power generated, according to the sign convention that power entering
the device is positive. The uncertainty in power is ±5 μW per phase.
Fig. 7. Frequency response of all the phases under Phase-1 excitation. The
measurement uncertainty in log(V ) is ±0.05.
VII. E XPERIMENTS U NDER D RIVEN E XCITATION
The first experiments performed on the EQS generator
were driven-excitation experiments. Under these conditions,
’s in Fig. 5 were applied with six function generators
the VDi
(Agilent 33220A), one for each phase. A 1-kΩ current-sense
resistor was placed in series with the voltage sources. The perphase real and reactive powers were measured with six Analog
. The inductors for
Devices AD835 multipliers at points VDi
this application were JW Miller Model 4671 inductors with a
nominal inductance of L = 8.2 mH, chosen to set the operating
frequency to about 400 kHz. For these inductors, the following
were measured to be the nominal model parameters: CL =
1.7 pF, RL = 40 Ω, RLp = 1 MΩ, and RC = 1 kΩ (see Fig. 5).
To further reduce the capacitive loading on the device and
make net generation possible, the voltage probes (Agilent
10440B 100:1 probes, 2.5 pF10 MΩ) used to measure wi
during device characterization were removed for this experiment. Therefore, CEij , i = j was reduced from approximately
4.5–2 pF per phase.
With the new CEij matrix, a nonlinear optimization was
performed on the model to find the power-optimal drive-voltage
amplitudes and phases, as well as the optimal speed and electrical frequency. All voltage magnitudes converged to their upper
bounds for most optimizations.
Fig. 9. Sum of the per-phase powers versus mechanical speed. Negative power
indicates power generated, according to the sign convention that power entering
the device is positive. The uncertainty in power is ±30 μW.
A. Experiments at Moderate Levels of Excitation
We found that the linear state-space model correlated well
with measured power output when we used moderate-excitation
levels on the generator phases. Fig. 8 shows the per-phase
power–speed relationship obtained when exciting the machine
with VDi = 1.6 Vpp and phase angles 0◦ , −30.4◦ , −110.1◦ ,
−195.7◦ , −217.7◦ , −254.6◦ at 402.9 kHz. The curve shown in
Fig. 9 is the real power sum of all the phases. In the moderateexcitation regime, the calculated sensitivity of peak power to
gap is about 400 μW per 1 μm of change in air gap. The good
model agreement suggests that the gap is close to the previously
fitted 4.15 μm. Negative power indicates generated power,
which in this setup was returned to the function generators. A
maximum of 108 μW ± 30 μW at 245 krpm was generated by
the system—the generator and its external electronics—in this
experiment. The corresponding voltages Vi on the electrodes
and wi at the device’s external electrical connections were
∼ 30 Vpp .
STEYN et al.: SELF-EXCITED MEMS ELECTRO-QUASI-STATIC INDUCTION TURBINE GENERATOR
429
B. Device Efficiency
The electromechanical model described earlier can be used
to estimate the power lost in various parts of the system
and to calculate the mechanical to net electrical efficiency
of the device. To determine the overall (airflow to electric)
efficiency of the device, the losses in the turbine and air gap
should also be taken into account; these are estimated from
the measured pressures and mass flow rates, assuming that the
flow through the turbine is adiabatic. At 245 krpm, a total
of approximately 300 mW enters the turbine in the airstream.
Turbine inefficiencies dissipate 219 mW. This is understandable, given that the design speed of the turbine is 2.4 Mrpm.
A further 54 mW is dissipated in air-gap viscous losses, with
26.7 mW accounting for journal- and thrust-bearing viscous
losses. The electromechanical model indicates that a negative
torque of 0.03 μN · m is produced by the air-gap electric fields,
corresponding to a mechanical power input to the generator of
790 μW at 245 krpm. Of this shaft power, 255 μW is lost in the
rotor conductor, and 535 μW enters the external circuit shown
in Fig. 5. Internal machine interconnect and wiring resistances
account for 75 μW of the losses. The bulk of the power from
the machine, 280 μW, is dissipated in the inductor core, with
inductor wiring and the combination of dielectric and proximity losses accounting for 50 and 22 μW, respectively. These
calculations yield an overall (airflow to electric) efficiency at
peak power of 0.036%. The low efficiency as compared with
macroscale systems reflects several factors, including operation
of the turbine far from its design point and the power-limiting
effects of carrier depletion in the rotor. The mechanical to net
electrical efficiency at peak power is 14%, not including viscous
losses in the machine’s air gap, or 0.2%, including the air-gap
viscous losses.
C. Results at Higher Levels of Excitation
The power generated under driven excitation was also measured as a function of excitation voltage for excitations as
high as 3 Vp−p . Fig. 10 shows the sum of the per-phase
powers versus the driving voltage squared for four different
excitation frequencies and the same set of phase angles as was
employed previously and a speed of 235 krpm. As the excitation
voltage increases, the generated power first increases and then
decreases. For two of the excitation frequencies examined, the
machine ceases to generate power. In contrast, the model from
Section V predicts that the generated power should increase as
the square of the excitation voltage. This trend is predicted to
increase until the electric field across the air gap reaches the
onset of breakdown at about an order of magnitude greater voltage than is experienced in these experiments. The discrepancy
between predicted and measured performance is attributed to
carrier depletion in the polysilicon rotor-conductor film, which
effectively increases the air gap; the electrode/air-gap/rotor conductor structure is analogous to the metal/oxide/semiconductor
structure in a MOS capacitor, in which the same phenomenon
occurs [16]. The increase in effective air gap has two effects.
First, since the effective air gap increases faster than the voltage
for sufficiently large voltages [17], an increase in the electrode
voltage can decrease the electric field in the gap and decrease
Fig. 10. Comparison of fitted model and experimental results for large drive
voltages. The measurement uncertainty is ±30 μW.
the power output. Second, the increase in effective air gap
decreases the device capacitance and modifies the system’s
resonance. This is consistent with the measured dependence of
power output on frequency and voltage. At low voltages, the
power output is highest at 411 kHz, near the system’s resonant
frequency, as expected. The higher voltage deviations from the
model in Section V are also most pronounced at 411 kHz,
because a given driving voltage produces the largest electrode
voltage when it is applied at the resonant frequency. At lower
excitation frequencies, the maximum power output occurs at
progressively higher values of the driving voltage, consistent
with the fact that the amplification of the driving voltage onto
the stator electrodes is reduced off-resonance.
The actual rotor gap remains constant to within 0.2 μm,
as evidenced by the nearly constant air flows through the
thrust-bearing gaps [10]; the depletion of the carriers in the
rotor conductor was incorporated into the model described in
Section V by replacing the actual air gap with an effective gap
that is a function of electrode voltage. The voltage-dependent
effective gap was used as a fitting parameter to fit the model
to the measured data at increased drive voltages. A strongly
saturating (tanh) fitting function was then fit to the effective
gap to determine the saturation voltage. At higher voltages,
as much as 0.7 μm of air-gap increase was needed to match
the data. Because this air-gap increase is greater than the rotor
conductor-film thickness, this indicates a fully depleted film and
a change in rotor conductivity at higher voltages. The change
in rotor conductivity was not accounted for in the model. The
smooth curves in Fig. 10 represent the revised model, including
the nonlinear rotor conductor. The maximum power output of
the generator was 192 μW ± 30 μW, recorded at an excitation
voltage of VDi = 2.4 Vp−p , which corresponds to voltages Vi
and wi of about 50 Vp−p .
VIII. E XPERIMENTS U NDER S ELF -E XCITATION
The performance of the machine was also measured under
self-excitation. All external driving voltages VDi were set to
zero, and the mechanical speed was increased until the phase
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Fig. 12. Self-excited EQS generator produced enough power to light up four
high-intensity LEDs on two of the phases, phases 4 and 5. The LEDs on phase 6
remain unlit. Picture taken with a Canon Powershot A80 camera in a dimly lit
room. Exposure time: 15 s, ISO speed 100, and f-stop 3.2.
Fig. 11. Eigenfrequency and average voltage magnitude versus speed for
the generator as measured at points wi defined in Fig. 5. The scatter in the
frequency data is attributed to small variation in the airgap due to presumed
nonidentical thrust-bearing pressures at the same operating speed. The uncertainty in frequency is ±1 kHz and in voltage is ±0.1 V.
voltages were self-excited through the amplification of random
fluctuations; in this mode of operation, the generator and its
load are electrically unstable. The model was first used to
predict the conditions (rotational speed and presence of various
measurement probes) under which self-excitation was expected
to occur. This was determined by examining the real parts
of the eigenvalues of the matrix A−1 B from (1). At speeds
greater than 215 krpm, the machine self-excited. Fig. 11 shows
the measured and predicted eigenfrequency over the range of
rotational speeds at which the frequency was measured. The
results show good agreement with the model, with the eigenfrequencies very close to the predicted values. Self-excitation
begins close to the predicted rotational speed for onset of selfexcitation; its end at about 300 krpm reflects the fact that no
measurements were made at higher rotational speeds because
of bearing-stability concerns. The voltages wi were measured
using low-capacitance probes, and the average voltage magnitude is plotted versus speed in Fig. 11. The maximum voltage
wi attained under self-excitation was approximately 29 Vp−p
and is limited by rotor-conductor depletion as described earlier;
the models indicate that the value of Vi is essentially the same
as that of wi . All of the power generated by the EQS generator
in these experiments was dissipated in the wiring resistances
and the inductors.
In separate experiments, the self-excited generator also provided power to an external load in the form of four highbrightness LEDs. Two LEDs were coupled to the points wi on
each phase through adjustable coupling capacitors. The coupling capacitances were adjusted until the LEDs on phases four
and five lit up; the LEDs on the other phases remained unlit.
Fig. 12 shows a photograph of the LEDs lit by the generator.
With the visibility threshold of each LED at approximately
35 μW, the power delivered to the four LED load is estimated
at 140 μW total.
IX. S UMMARY AND C ONCLUSION
The results reported here demonstrate the feasibility of an
EQS induction micromachine as a generator. The amount of
power it can generate is limited by its external and internal stray capacitances. It is therefore necessary to minimize
all the strays and accurately model those that remain along
with their imbalance. This also motivated the use of thick
(10–20 μm) PECVD oxide films for electrical isolation in the
present device. Power generation could only be attained at high
operating speeds (> 200 krpm) and with a metal stator for lowresistive losses. Our generator addressed these requirements by
being the first fully bonded MEMS EQS induction machine
with a metal stator structure. This stator structure had a PECVD
oxide surface as a bond surface, where surface bondability
was achieved after the fabrication of that layer. A precise
20-μm-wide 300-μm-deep journal bearing allowed for stable
operation beyond the synchronous speed. These or similar
techniques to control the parasitic capacitances, to limit resistive losses, and to ensure high-speed operation are expected
to be key components of creating effective EQS machines in
the future.
Creating an inherently phase-balanced machine design and
employing accurate detailed models of its performance were
also shown to be key aspects of successful operation of the EQS
machine as a generator. A well-balanced machine is important
because it minimizes electric losses and operational challenges
of understanding and correcting for the machine’s fundamental
imbalances. Accurate modeling, including inductor models that
are accurate over a wide frequency range, enables the total
model to be used to guide generator operation. This paper
demonstrates that it is possible to estimate the external strays
and other parameters—in this case, a total of 23—from a
suitable set of frequency-domain experiments using a nonlinear
least squares technique. The calibrated models are in agreement
with the measured results, and similar models with parameters
calculated from first principles can be used to design future
devices of this kind.
The device presented here was operated for tens of hours over
a speed range of 200–300 krpm and a drive-voltage range of
VDi = 0−3 Vpp . No degradation in performance was observed.
The maximum power recorded was 192 μW. At VDi = 1.6 Vpp ,
108 μW was produced, and the machine terminal voltages
wi were ∼ 30 Vpp . At the terminals, 535 μW was generated.
At both high-driven voltages (wi ∼ 50 Vp−p ) and under selfexcited operation, a significant power-limiting carrier-depletion
effect was identified. Scaling to the design conditions, using the
linear model and assuming that a better rotor conductor can be
STEYN et al.: SELF-EXCITED MEMS ELECTRO-QUASI-STATIC INDUCTION TURBINE GENERATOR
found, it is predicted that, with a terminal voltage of 600 Vpp ,
at 900 krpm, this device could produce 0.5 W at the terminals at
an overall device efficiency of 15%. In addition, the possibility
of self-excitation, without the need for external drive electronics, greatly simplifies its practical implementation for powergeneration applications.
The results obtained in this paper suggest that EQS generators have significant potential for integration into MEMS
gas turbine generators that output mechanical power at the
several-Watt scale. The present EQS generator’s power output,
while small, has the potential for a three orders of magnitude
increase with the introduction of a second-generation linearrotor conductor, making it consistent with the power scales of
MEMS engines. Although MEMS magnetic generators are expected to offer somewhat higher powers and somewhat higher
efficiencies than future EQS generators (of order 60% rather
than 45% for the best projected EQS generators) [18], the
EQS generator offers important advantages. The fabrication
of the EQS generator is fundamentally CMOS compatible,
and integration of the generator into a silicon engine will not
require the creation of additional technologies beyond a secondgeneration rotor conductor and the technologies demonstrated
in this paper. Additional advantages include the small size of
the EQS device, the use of a light rotor that is readily supported
by air bearings, and compatibility with the high temperatures in
a fuel-burning engine.
[7] C. Livermore, A. R. Forte, T. Lyszczarz, S. D. Umans, A. A. Ayon, and
J. H. Lang, “A high power MEMS electric induction motor,” J. Microelectromech. Syst., vol. 13, no. 3, pp. 465–471, Jun. 2004.
[8] T. L. Willke, “Self-excited electrostatic generator,” M.S. thesis, MIT,
Cambridge, MA, 1968.
[9] L. G. Fréchette, S. A. Jacobson, K. S. Breuer, F. F. Ehrich, R. Ghodssi,
R. Khanna, C. W. Wong, X. Zhang, M. A. Schmidt, and A. H. Epstein,
“High-speed microfabricated silicon turbomachinery and fluid film bearings,” J. Microelectromech. Syst., vol. 14, no. 1, pp. 141–152, Feb. 2005.
[10] C. J. Teo, “Bearings for microturbomachinery,” Ph.D. dissertation, MIT,
Cambridge, MA, 2005.
[11] H. Q. Li, N. Savoulides, L. Ho, S. A. Jacobson, R. Khanna, C.-J. Teo,
L. Wang, D. Ward, A. H. Epstein, and M. A. Schmidt, “Fabrication of
a high speed microscale turbocharger,” in Proc. Hilton Head Solid State
Sens., Actuator Microsyst. Workshop, Hilton Head Island, SC, Jun. 2004,
pp. 258–261.
[12] R. Ghodssi, L. G. Fréchette, S. F. Nagle, X. Zhang, A. A. Ayon,
S. D. Senturia, and M. A. Schmidt, “Thick buried oxide in silicon
(TBOS): An integrated fabrication technology for multi-stack waferbonded MEMS processes,” in Proc. 10th Int. Conf. Solid-State Sens.,
Sendai, Japan, Jun. 1999, pp. 1456–1459.
[13] S. F. Bart and J. H. Lang, “An analysis of electroquasistatic induction
micromotors,” Sens. Actuators, vol. 20, no. 1/2, pp. 97–106, Nov. 1989.
[14] K. Nabors, S. Kim, J. White, and S. D. Senturia, FastCap User’s Guide.
Cambridge, MA: Res. Lab. Electron., MIT, 1992.
[15] J. L. Steyn, “A microfabricated ElectroQuasiStatic induction turbinegenerator,” Ph.D. dissertation, MIT, Cambridge, MA, 2005.
[16] S. M. Sze, Semiconductor Devices, Physics and Technology. Hoboken,
NJ: Wiley, 1986.
[17] R. F. Pierret, Semiconductor Device Fundamentals. Reading, MA:
Addison-Wesley, 1996.
[18] S. Das, “Magnetic machines and power electronics for power MEMS
applications,” Ph.D. dissertation, MIT, Cambridge, MA, 2005.
J. Lodewyk Steyn received the B.Eng. degree in mechanical engineering from the University of Pretoria,
Pretoria, South Africa, in 1998, and the S.M. and
Ph.D. degrees from Massachusetts Institute of Technology, Cambridge, in 2002 and 2005, respectively.
He is currently the Lead MEMS Design Engineer
with Pixtronix Inc., Andover, MA, where he is currently developing low-power MEMS-based directview displays for portable electronic devices. He
has a keen interest in engineering in general and,
in particular, in MEMS design, fabrication, and
ACKNOWLEDGMENT
The authors would like to thank T. Lyszczarz, J. Yoon, and
the late T. Forte of the MIT Lincoln Laboratory for their contributions to the fabrication of the stator. They would also like to
thank C. J. Teo for operating the spinning generator at speeds
up to 850 krpm. They would also like to thank G. Donahue
for the journal-bearing process development. They would also
like to thank C. Law for providing the 3-D solid models
and rendering under the MIT UROP program. All microfabrication was performed at the MIT Microsystems Technology
Laboratories (MTL) and at the Micro Electronics Laboratory
(MEL) at MIT Lincoln Laboratory. Opinions, interpretations,
conclusions, and recommendations are those of the authors and
are not necessarily endorsed by the United States Government.
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pp. 331–338, Nov. 1990.
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characterization.
Sam H. Kendig received the S.B. degree in electrical
engineering from Massachusetts Institute of Technology, Cambridge, in 2006.
He is currently with Bose Corporation,
Framingham, MA, where he is developing homeentertainment products. His interests include design
of MEMS and analog electronics.
Ravi Khanna received the B.S. degree in physics in
1983 and the M.S. and Ph.D. degrees in electrical
engineering in 1992 from Pennsylvania State University, University Park.
From 1992 to 1998, he was a Senior Device and
Process Engineer with Skyworks Solutions, Woburn,
MA, where he oversaw the design, fabrication, and
testing of microwave-semiconductor components.
From 1998 to 2004, he enjoyed the challenges of
MEMS process development and implementation on
the MIT Micro-Engine and MicroRocket programs.
He is currently with BAE Systems, Lexington, MA, where he is working in
both production and development of infrared imaging systems.
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Stephen D. Umans (S’67–M’75–SM’82–F’95) was
born in Cleveland, OH, on November 10, 1948.
He received the S.B. and S.M. degrees in electrical
engineering and the Sc.D. degree in electrical engineering from Massachusetts Institute of Technology
(MIT), Cambridge, in 1972 and 1976, respectively.
Recently, he was a Principal Research Engineer
with the Electromechanical Systems Laboratory and
the Electrical Engineering and Computer Science
Department, MIT. He is currently an independent
Consultant, with specific focus in the areas of
electromechanics, electric power systems, and electric machinery. He is the
coauthor of the textbook Electric Machinery (McGraw-Hill, 1990).
Jeffrey H. Lang (F’98) received the S.B., S.M.,
and Ph.D. degrees from the Department of Electrical
Engineering and Computer Science, Massachusetts
Institute of Technology (MIT), Cambridge, in 1975,
1977, and 1980, respectively.
Since 1980, he has been with the faculty of MIT,
where he is currently a Professor of electrical engineering and computer science. From 1991 to 2003,
he was the Associate Director of the MIT Laboratory
for Electromagnetic and Electronic Systems. His research and teaching interests focus on the analysis,
design, and control of electromechanical systems with an emphasis on rotating
machinery, microscale (MEMS) sensors, actuators and energy converters, and
flexible structures. He has written over 200 papers and holds 12 patents in
the areas of electromechanics, MEMS, power electronics, and applied control.
He is the coauthor of Foundations of Analog and Digital Electronic Circuits
(Morgan Kaufman, 2005).
Dr. Lang was an Associate Editor of Sensors and Actuators from 1991 to
1994. He was the recipient of four Best Paper Prizes from IEEE Societies. He
is a former Hertz Foundation Fellow.
Carol Livermore received the B.S. degree from the
University of Massachusetts, Amherst, in 1993 and
the A.M. and Ph.D. degrees from Harvard University,
Cambridge, MA, in 1995 and 1998, respectively, all
in physics.
From 1998 to 2002, she was a Postdoctoral
Associate and then a Research Scientist with
Massachusetts Institute of Technology (MIT),
Cambridge. Since 2003, she has been on the faculty of MIT, where she is currently an Associate
Professor with the Department of Mechanical
Engineering. Her research interests include power MEMS and the development
of techniques and applications for nano- and microscale self-assembly.