MECH 466

Microelectromechanical Systems
University of Victoria
Dept. of Mechanical Engineering

Lecture 5:
Electrostatic Sensors and Actuators

© N. Dechev, University of Victoria 1

Overview

Introduction to Electrostatics
Overview of Electrostatic Actuators and Sensors
Parallel Plate Capacitors
Electrostatic Interdigitated Finger Capacitors (Comb-Drives)

© N. Dechev, University of Victoria 2

 Introduction to Electrostatic Transducers

Electrostatic sensors and actuators operate on the principle of

electric charge.
Electrostatics work well for micro-scale devices, since the
(surface area/volume) ratio is higher for micro-devices.
The electrostatic effect is based on surface area, while mass is
based on volume, and hence electrostatic force is good for
microsensing and microactuation.

Accelerometer [Analog Devices] DLP Micromirror Matrix [Texas Instruments]

© N. Dechev, University of Victoria 3

Introduction to Electrostatic Transducers

For ‘sensors’, capacitive devices can be used.

- A typical capacitor is comprised of two conductive elements,
physically separated from each other, using some kind of
dielectric material.

A
d

- The capacitance of a capacitor may be varied by:

Dielectric Material Properties
______________________
Overlap Area A, of Electrodes
______________________
Distance d, between Electrodes
______________________

© N. Dechev, University of Victoria 4

 Introduction to Electrostatic Transducers

For ‘actuators’, movable structures carrying accumulations of

electric charge can be used.
There are two possible cases for using electric charge to generate
force, and hence motion.
Consider two parallel plates.

Attractive Force Repulsive Force

Positive Charge Positive Charge
+ + ++ + + + + ++ + +
+
+ + + + + + + + ++ +
+ +
+ + + + + + + + ++ +
+
++ + + + ++ + +
+ + + + + + + ++
- - - - - - - -- - + ++ + + + + + +
- - - - - ++ + + + ++
Negative Charge - - - - - Positive Charge + + + +

© N. Dechev, University of Victoria 5

Electrostatic Micromotor

One of the first electrostatic actuators was a micromotor.

Consider the principle of operation:
- Central rotor has one charge.
- Radial stator poles have opposite charge.
- Six stator phases (pair of poles) as shown below, are turned
on and off in a sequence to cause the rotor to turn.

1 1 1
6 2 6 2 6 2

5 3 5 3 5 3

4 4 4 4 4 4

3 5 3 5 3 5

2 6 2 6 2 6
1 1 1

(Shown above) Single Phase Driving Sequence: 1,2,3,4,5,6,1,2,3,4,5,6,...

(Alternate) Dual Phase Driving Sequence [1,4], [2,5], [3,6], [1,4], [2,5], [3,6],...
© N. Dechev, University of Victoria 6
 Electrostatic Micromotor

Movie of Electrostatic Motor, (720 stator poles)

[M. Basha, U of Waterloo]

SEM of an early Electrostatic Motor

[Mehregany, MIT]

© N. Dechev, University of Victoria 7

Electrostatic Comb-Drive

Electrostatic actuators can also be used to create ‘linear motion’

using a ‘comb-drive’ that makes use of interdigitated fingers.
The principle of operation:
- Central comb has one charge.
- Two outer combs are sequenced with opposite charge.

Movie of Comb-Drive Actuator

Generic Comb-Drive (Sensor or Actuator) [J. Levitan, MIT]
[D. Freeman, MIT]

© N. Dechev, University of Victoria 8

 Electrostatic Transducers

Benefits of electrostatic devices:

- simplicity
- very low power use for low frequency applications
- fast response:
- speed is governed by the charge and discharge time
constants, which are small for good conductors.
- switch time of 21us for DMDs.
- deflection can be accurately controlled
There are also disadvantages:
- Actuators require drive voltages in the 50 - 150 Volt range.
- Sensors require carefully designed circuits to measure
capacitance change in presence of noise and interference.
- Static capacitance values are in the picoFarad range,
while capacitance changes are in femtoFarad range.
- Large surface area is required for comb-drives to generate
forces equivalent to other micro-actuators.
© N. Dechev, University of Victoria 9

Parallel Plate Electrostatic Devices

Example of a parallel plate electrostatic system, is the DMD

(Digital Micromirror Device), developed by Texas Instruments.

DMD Operation Schematic,

[Texas Instruments]

© N. Dechev, University of Victoria 10

 Parallel Plate Electrostatic Devices

Micro-Mirror
Element (Pixel)
Micro-Mirror
Removed

Micro-Mirror
Compliant Hinge

Micro-Mirror
DLPTM Chip Actuator

DMD Operation [Texas Instruments]

© N. Dechev, University of Victoria 11

Parallel Plate Capacitors

Consider an “ideal” parallel plate capacitor:

A
Where: A - Overlap area of two plates
E d E - Electric Field
d - distance between the two plates

A dielectric material will occupy the space between the two plates:

The ‘Relative’ electrical permitivity is defined as:

The permitivity of the material is:

Where , is the permitivity of free space (vacuum)

© N. Dechev, University of Victoria 12

 Parallel Plate Capacitors

A
E d

The capacitance between two plates is defined as:

Stored Charge
=
Electrostatic Potential

The electric energy stored in the capacitor is:

© N. Dechev, University of Victoria 13

Parallel Plate Capacitors

To obtain an expression for capacitance for the parallel pales, we

can use Gauss’s Law, where the electric field:

This can be substituted into the capacitance equation to obtain:

© N. Dechev, University of Victoria 14

 Parallel Plate Capacitors

By measuring C accurately, we can sense changes in A (area),

Permittivity, or d (distance between plates).
For example, Permittivity of a material can be influenced by:
- Humidity
- Chemical reactions
- Temperature
Also, changes in the overlap of the two plates, or changes in the
distance between the plates, can be made by:
- Static pressure
- Acceleration
- Other physical phenomena

© N. Dechev, University of Victoria 15

Parallel Plate Capacitors

The force due to electrostatic attraction or repulsion between the

plates is important to determine, and is defined by:

If the plates move along the axis normal to their surface, the
variable of displacement is d. Therefore:

Solving:

© N. Dechev, University of Victoria 16

 Parallel Plate Capacitors

Example of force between two plates. (Example 4.1)

See Class Notes

© N. Dechev, University of Victoria 17

Interdigitated Finger Capacitors

Diagram of Comb-Drive:
wt xo
One Side of Comb

Lo
Lc
t

Other Side of Comb

© N. Dechev, University of Victoria 18

 Interdigitated Finger Capacitors

Modeling of Comb-Drives

Mechanical Connection
Between Combs
Km

C
Cf

Where: C - Normal Capacitance Between Beams

Cf - Fringe Capacitance (Highly Non-linear)

One Comb is Anchored

A mechanical spring constant, Km, represents the stiffness of the

compliant mechanism between the two combs

The two types of capacitance, C, and Cf, both have substantial

contributions to the overall capacitance of the device.
© N. Dechev, University of Victoria 19

Interdigitated Finger Capacitors

The total capacitance of the system is given by:

For the previous diagram:

There are two main types of Comb-Drives:

- Transverse
- Longitudinal

© N. Dechev, University of Victoria 20

 Transverse Comb-Drive

The design of the flexure mechanism will determine the system

stiffness and hence axis of motion
Anchor
Points
Deflected
Beams
Flexible Km (y-axis)
Beams High Stiffness

Km (x-axis)
Low Stiffness

δx

(a) (b)

© N. Dechev, University of Victoria 21

Transverse Comb-Drive

y
Lo
x

xo x

When the upper comb is deflected to the right, the capacitance

will change between the fingers as follows:
relative motion
Capacitance of
left side:

Csr
Capacitance of
right side:
Csl
© N. Dechev, University of Victoria 22
 Transverse Comb-Drive

The total capacitance is defined as:

Note: under equilibrium conditions, the net change in capacitance

will be zero.

However, during motion, the rate of capacitance change can be

measured, termed the displacement sensitivity, Sx:

If the comb-drive is used as an actuator, the force can be

represented as:

© N. Dechev, University of Victoria 23

Longitudinal Comb-Drive

y
Lo
x
yo

+y

The capacity change associated with a single finger is:

Note: under equilibrium conditions, the net change in capacitance

will be a finite amount.

© N. Dechev, University of Victoria 24

 Longitudinal Comb-Drive

The displacement sensitivity in the longitudinal direction, Sy, is

defined as:

If the longitudinal comb-drive is used as an actuator, the force can

be represented as:

Note: The solution to these equations is not trivial.

© N. Dechev, University of Victoria 25

Computation of Comb-Drive Values

To compute values such as force, displacement sensitivity, and

other parameters, numerical methods are required.
The contribution from ‘fringe capacitance’ is substantial, and
cannot be ignored.
However, ‘fringe capacitance’ is highly non-linear and changes
with different initial conditions and boundary conditions.

Electric Field Plot

[C. Liu]
© N. Dechev, University of Victoria 26
 Computation of Comb-Drive Values

Electromagnetic FEA (finite element analysis) is often used to

compute the electric fields and intensities, and subsequently to
determine capacitance, force and other parameters.

Electric Field Isolines

[ANSYS]

© N. Dechev, University of Victoria 27

Linear Actuators based on Comb-Drives

Linear Actuator
[Sandia National Laboratories]

Read Case 4.9 in Textbook. Example of how comb-drives are

used for linear actuation of a Gear Rack, via a Pinion Gear.

Rotational Comb-Drives
Rotational Comb-Drive
[ALGOR FEMPRO]

© N. Dechev, University of Victoria 28