Unfortunately, there is silicon, and there is silicon.  The growth
process, and subsequent thermal steps in its fabrication, affect
fracture strength.  For instance, magnetic Czochralski starting material
is better than CZ, because (I think) it has a lower concentration of
oxygen, below 20 ppm.  Also, thermal processing above 1150 degC, ideally
in an argon ambient, improves fracture strength (see below).

Also, silicon is a crystal.  Fracture strength is a function of
crystallographic direction.

Also, surface texture and surface film (e.g., SiO2) affect the
initiation of a crack at a surface.

What this all means:  you must remember that there is a *distribution*
of fracture strength for any ensemble of crystalline structures,
ostensibly fabricated 'the same'.  This distribution has a mean, and a
standard deviation.  The mean can be increased somewhat using starting
material with lower point defect concentrations.  The standard deviation
can, to a certain extent, be made smaller by using thermal processing in
inert ambient at temperatures above 1150 degC.  Control of surface
roughness and use/control of surface films is also important.

See:  JMEMS reference by CA Wilson and P Beck (HP).  Various works by
Alissa Fitzgerald (AM Fitzgerald & Assoc) and Chris Muhlstein (Penn
State).  I've written some on the subject, in SPIE MEMS proceedings.

Bottom line:  there is no 'safety factor', except insofar as you build
devices, measure at what fracture strength they break (measure the
distribution function, in other words), and either specify
pressures/forces that avoid the mean of the fracture strength minus,
say, 3 sigma, or re-design the structure to survive higher
pressures/forces.

PS:  It has never been shown experimentally, but I have a strong
suspicion that isotopically pure silicon will have a much higher
fracture strength than 'regular' silicon (with composition of isotopes
as found in nature).  Isotopically pure silicon has been shown to have
much higher electrical mobility, and much higher thermal conductivity,
so it should have higher fracture strength. Unfortunately, isotopically
pure silicon is very expensive...

---
Albert K. Henning, PhD
Director of MEMS Technology
NanoInk, Inc.
215 E. Hacienda Avenue
Campbell, CA  95008
408-379-9069  ext 101
ahenning@nanoink.net


-----Original Message-----
From: Brian Stahl [mailto:bstahl@mrl.ucsb.edu]
Sent: Tuesday, November 10, 2009 9:40 AM
To: General MEMS discussion
Subject: Re: [mems-talk] Si stress-strain relationship and allowable
stress

Hi Karolina,

Single-crystal silicon can be considered a brittle material at room
temperature, but at elevated temperatures it flows plastically at
stresses
much lower than its room-temperature yield stress.  This is important if
your structure will see elevated temperatures.  I think you can safely
assume that silicon behaves linearly as long as the applied stresses are
several percent below the yield/fracture stress (the linear
elastic/plastic
transition is not always sharply defined).  As for calculating your
working
stress, 3) is correct - take the fracture or yield stress of silicon (to
be
on the safe side you could take whichever value is lower) and divide it
by
your desired factor of safety.  Safety factors vary depending on the
application, and no one value can be quoted as being correct.  If you
require higher reliability or if your device might be subjected to loads
in
excess of the design load, you might want a higher safety factor - it
all
depends on your application.

Good luck,

Brian Stahl