Wavefront Correctors - Adaptive Optics for Biological Imaging - page 131

Anchor

Sacrificial layer

Substrate

Structural layer

Release etch

FIGuRE 8.22 Cross.section.of.the.surface.micromachining.process.showing.the.gap.between.the.structural.layer.
and.the.substrate.that.is.deined.by.the.sacriicial.layer.ater.the.release.etch..he.thin-ilm.deposition.processing.
that.is.used.in.surface.micromachining.limits.the.sacriicial.layer.to.several.micrometers.in.thickness.

A

+Q

+Q g 0

z

-Q

z g 0

-Q

FIGuRE 8.23 Parallel.plate.capacitor.with.an.area. A ,.charge. Q ,.and.an.initial.gap. g 0 ..When.connected.to.a.voltage.
source,.one.plate.acquires.a.negative.charge.( −Q ),.and.the.other.plate.acquires.a.positive.charge.( +Q ),.leading.to.an.
attractive.force.between.the.plates..he.top.plate.moves.in.the. z .direction.and.the.gap.is.decreased.from.its.initial.
value.of. g 0 .

where.the.capacitance.of.a.parallel.plate.capacitor.is.given.by

A
g

A

. .

C = ε = ε (8.6.2.2)

0 0

g − z

0

ε 0 .is.the.dielectric.permittivity.of.free.space.(8.85.×.10 −12 .F/m),. g .is.the.distance.between.the.plates.(m),.
and. A .is.the.area.of.the.plates.(m 2 ).
he.incremental.work.d U .done.in.charging.the.capacitor.by.transferring.an.incremental.charge.d Q .
from.one.plate.to.the.other.through.a.voltage. V .is.given.by

d U V Q = d (8.6.2.3)

. .

Substituting.for. V ,

Q Q
C

d

d U V Q = d = (8.6.2.4)

. .