Biomedical Engineering Reference
In-Depth Information
Substituting.for.
k
.and.solving.for.
z
,
V
2
ε
A V
g
2
(
8.6.2.19
)
.
.
0
ε
A
z
=
(
)
(
)
0
3
2
g
−
z
2
−
z
0
0
g
z
=
0
3
.
.
(8.6.2.20)
When. one-third. of. the. initial. gap. has. been. closed,. the. plates. snap. together. or. pull-in.. his. pull-in.
instability.limits.the.useful.range.of.parallel.plate.electrostatic.actuators.with.linear.springs..For.parallel.
plate.electrostatic.actuators.formed.in.surface.micromachining.processes,.the.initial.gap.is.deined.by.
the.sacriicial.layer.thickness,.which.is.practically.limited.to.a.few.micrometers,.so.that.the.useful.actua-
tion.range.is.typically.less.than.a.micrometer,.unless.a.nonlinear.spring.or.leveraged.bending.is.used.
(Hung.1999)..To.ind.the.pull-in.voltage,.the.gap.at.pull-in,.
g
0
/3,.can.be.substituted.into.Equation 8.6.2.18.
and.solved.for.the.voltage:
V
2
V
g
2
27
8
ε
A
.
2
.
0
3
k
=
ε
A
=
ε
A
=
V
(8.6.2.21)
(
)
(
)
0
3
0
3
g
g
−
z
2
3
0
0
z g
=
3
0
8
27
kg
3
.
.
(8.6.2.22)
V
pull-in
=
ε
A
0
8.6.4 electrostatically Actuated Membrane Mirrors
Example. of. an. MEMS. DM. that. uses. bulk. micromachining. is. the. membrane. mirror. developed. at. Delt.
University,. which. was. later. commercialized. by. Flexible. Optical. B.V.,. now. known. as. Flexible. Optical.. An.
.aluminum-coated.membrane.is.deined.in.a.silicon.chip.using.bulk.micromachining..he.silicon.chip.is.then.
bonded.to.a.substrate.with.control.electrodes.through.a.spacer.layer..he.spacer.layer.deines.a.gap.across.
which.a.bias.voltage.is.placed,.which.causes.the.membrane.to.delect.under.electrostatic.forces.(Figure.8.26).
A.similar.approach.is.used.by.Agile.Optics.in.their.membrane.mirror,.as.shown.in.
Figure.8.27
..Here.
a.silicon.frame.supports.a.silicon.nitride.membrane.that.is.approximately.1.μm.thick..Silicon.nitride.is.
an.insulating.layer.that.is.typically.used.as.masking.material.for.wet.anisotropic.bulk.micromachining.
Control electrodes
Al-coated membrane
Si chip
Substrate
PCB
Spacer
Control
voltages
V
2
V
1
V
3
V
n
Bias voltage
V
b
FIGuRE 8.26
MEMS. membrane. mirror. fabricated. with. bulk. micromachining.. A. silicon. chip. with. an.
.aluminum-coated.mirror.membrane.supported.along.the.edges.is.bonded.to.a.substrate.with.a.spacer.layer..he.
thickness. of. the. spacer. layer. deines. the. gap. across. which. an. applied. bias. voltage. induces. an. electrostatic. ield,.
.causing.the.mirror.membrane.to.delect..he.control.electrodes.can.be.individually.biased.to.control.the.shape.of.
the.mirror..(Credit:.Flexible.Optical.B.V.,.he.Netherlands.)
