I have to apologize for my math in the reply below - I made a pretty big error
with decimal placement when calculating the temperature and thickness specific
reistivity.  I said that 200,000 ohm-m with a 0.5 µm film gave a value of 1,000
ohm-m2, when in fact it should be (200,000 ohm-m * 0.0000005 m) = 0.1 ohm-m2.
Only 4 orders of magnitude difference:-)

At this point, my assumption of the oxide layer dominating is incorrect -
instead, the pyrex/borofloat glass resistivity will dominate.

Also, I made a second mistake - my estimation of the resistivity as a power
function of temperature was probably flawed in that I used "ºC" rather than
"ºK". Biasing the function for ºK, the resistivities now look more like:

350      2.3e7
400      6.2e6
500      5.7e5

These values are still not major hindrances.  Even at 350ºC, the layer modified
resistivity is 11.5 ohm-m2.  With a standard process voltage of 500V, this would
allow 43A/m2 (or an initial current on a 200mm wafer of 1.37A - still not a
major factor in an anodic bond - the glass would still be the current limiter).
Even if the estimation of the resistance is off by two orders of magnitude, the
anodic bond process should still run.

Please note that the values used for resistivity were drawn from the following
web-page:

http://hypertextbook.com/physics/electricity/resistance/

Best Regards,
Chad Brubaker

EV Group
invent * innovate * implement
Senior Process Technology Engineer - Direct: +1 (480) 305 2414, Main: +1 (480)
305 2400 Fax: +1 (480) 305 2401
Cell: +1 (602) 321 6071
E-Mail: [email protected], Web: www.EVGroup.com


-----Original Message-----
From: [email protected] [mailto:[email protected]] On
Behalf Of Brubaker Chad
Sent: Thursday, October 02, 2008 8:31 AM
To: General MEMS discussion
Cc: Brubaker Chad
Subject: Re: [mems-talk] Anodic bonding

That kind of anodic bond is definitely possible - the general elements for the
physics still exist.  The requirement is that a certain amount of current be
achieved to cause sodium migration away from the bond interface. The biggest
limitation will be the resistance of the oxide.  Luckily, the resistance of the
oxide is a function of temperature.

At room temp, SiO2 has a resistivity of ~1E13 ohm-m.  But at 600C, that drops to
~70,000 (and all the way to .004 at 1300ºC).  Using a power based function (only
an approximation, but the closer to known values, the more accurate it is), we
can estimate 200,000 ohm-m at 500ºC, or 650,000 ohm-m at 400ºC.

Now, one thing to keep in mind - resistance is resistivity /area.  However, as
we are primarily concerned with current flux (since current will increase with
the area of the wafer), resistivity is the best term to use.

At 200,000 ohm-m, .5 µm of oxide will provide 1000 ohm-m2 of resistivity.  Using
a 2000V potential, assuming the oxide resistance is dominating initially, this
would still allow a current density in the initial stages of the bond of2A/m2,
which is sufficient for anodic bonding (this translates to 63mA for a 200mm
wafer - definitely well within bondable range).

If we lower the bonding temperature to 400ºC, then the current flux drops to
.61A/m2 - the bond may work at this point, but I wouldn't be sure.

Best Regards,
Chad Brubaker