Several observations:

First, Reza hasn't said anything about the application, and for all we know
this might not be a pressure sensor and the cavity might be vented to the
outside, eliminating any pressure differential and the resulting bowing
(which wouldn't be much anyway: assuming 53um thick square membrane, 1.6mm
side length, 1 atmosphere pressure differential, (100) silicon E=168GPa and
nu=0.28, deflection = 0.015975*P*(1-nu^2)*L^4/(E*t^3) = 0.4 microns).  If
the cavity is sealed and the bonding is done at 1ATM, worst case scenario is
that the membrane bulges outward.  If bonding is done in vacuum, worst case
scenario is that the membrane bulges inward 0.4 microns when exposed to
atmosphere.

Secondly, depending on how you apply force to the silicon wafer to hold the
two substrates together during the bonding process, you may or may not see
any deflection of the membrane due to this force.  I'm assuming that you
apply a mechanical (rather than hydrostatic) force of ~300psi to the wafer
with a press or something like that.  If this is the case, you shouln't see
bowing of the membrane from this force.  If somehow there is a 300psi
pressure loading on the membrane, by my calculations that will result in 7.8
microns of deflection.

Thirdly, even if you have a 1200V bias across the 10 micron cavity (and
that's not the case, because either the glass isn't a conductor and your
electric field = 1200V/glass thickness or the glass is a conductor and your
electric field in the cavity = 0 because you have the glass in contact with
the silicon around the cavity), that would only result in a 0.25 micron
deflection in the membrane (deflection =
0.015975*(1-nu^2)*epsilon*V^2*L^4/(2*E*d^2*t^3) )

Even if all these are true, by my calculations the membrane will only
deflect 0.4 microns + 7.8 microns + 0.25 microns = 8.5 microns.

So, it's possible that you'll have some deflection of the membrane depending
on your bonding conditions, but I doubt that the two electrodes would
touch.  If you're worried about gold-gold interdiffusion bonding, you could
always eliminate the electrode on the membrane and use the membrane itself
as the other parallel plate, as the gold pad on the silicon are electrically
shorted anyway (unless you have gold-on-oxide-on-silicon).

Feel free to contact me if you have any more questions.

Regards,

Brian C. Stahl
Graduate Student Researcher
UCSB Materials Research Laboratory
brian.stahl@gmail.com / bstahl@mrl.ucsb.edu
Cell: (805) 748-5839
Office: MRL 3117A


On Wed, Feb 4, 2009 at 3:54 PM, Brubaker Chad wrote:

> I'd say that the odds are good that the Si membrane may be drawn towards
> the glass - the net negative charge at the surface of the glass wafer will
> probably draw it.  Whether it will be enough for contact is a different
> question
>
> However, for the second part of the question, I'll have to say "that
> depends".  At a bonding temperature of 350ºC, probably not, since the
> interdiffusion of gold into gold is still fairly low.
>
> However, if the bond takes place at 400ºC, there may be more of an issue.
>  The electrostatic forces that occur during the anodic bond my be sufficient
> to bring the two into intimate contact, which may allow for interdiffusion
> between the gold layers (this is the same mechanism that occurs when
> performing a gold-to-gold thermocompression bond, which is also typically
> performed in the neighborhood of 400ºC, and is sufficient to form a hermetic
> seal).
>
> Bonding in air vs. vacuum can definitely change the balance of things.  In
> the case of bonding with air, I can see two significant effects.  If we
> assume that the substrates are already in very intimate contact when the
> voltage is turned on, then the air inside the cavity will have no where to
> go.  So, for the first effect, if the electrode starts to flex towards the
> glass, then the air on the glass side will increase in pressure, creating
> some resistance to further flexing.  Once the bonding is done, this will
> promote the movement of the electrode back to its original position
> (although from then on, external variations in air pressure will cause
> flexure to the electrode - this is how pressure sensors work).
>
> If the substrates are not in completely intimate contact prior to voltage
> (due to wafer warp or TTV issues, etc.), then at least some of the air in
> the cavity will escape.  There will be less resistance to flexing of the
> electrode towards the glass.  Plus, upon completion of the bond, air can no
> longer re-enter the cavity (since the electrostatic forces of bond will
> generaly overcome all but severe warpage and TTV), and so the cavity will
> effectively contain a partial vacuum.  So , when the exterior is
> re-pressurized to atmospheric, the eletrode will remain partially deflected
> towards the glass, since the pressure differential will push on it.
>
> Wnen bonding in vacuum, you basically guanrantee that the second case is
> true - the only difference is, instead of having a partial vacuum in the
> cavity, you will have a nearly complete vacuum in the cavity- you will
> pretty much always have flexure of the electrode towards the glass.
>
> Best Regards,
> Chad Brubaker