Silicon is a cubic crystal; as such a measure such as "Young's modulus" is
insufficient to describe its anisotropic behavior. In terms of modeling, one
should use an anisotropic elastic description for the material either in the
crystal axes ([100],[010],[001] directions as base directions for the elastic
constants) or in axes which may be more natural for the problem you are looking
at. In your case, you are dealing with {110} wafers, which would make the
[110], [1,-1,0] and [001] crystal directions more natural, perhaps. Note that
in this case, you will have the "x_1" direction normal to the wafer, and "x_2 &
x_3" will lie in the plane of the wafer. In this orientation, the material
appears orthotropic rather than cubic, so it requires a few more constants to
characterize. In either case, the elastic constants are well known.
If you choose to use the cubic crystal axes ([100], [010], [001]), the 6x6
stiffness tensor is (in units of GPa),
[ 166 64 64 0 0 0 ]
[ 64 166 64 0 0 0 ]
[ 64 64 166 0 0 0 ]
C_ij = [ 0 0 0 80 0 0 ]
[ 0 0 0 0 80 0 ]
[ 0 0 0 0 0 80 ]
(In other words, C_11 = 166 GPa, C_12 = 64 GPa, C_66 = 80 GPa.)
If you choose to use the rotated axes ([110], etc.), the stiffness tensor is
[ 194 35 64 0 0 0 ]
[ 35 194 64 0 0 0 ]
[ 64 64 166 0 0 0 ]
C_ij = [ 0 0 0 80 0 0 ]
[ 0 0 0 0 80 0 ]
[ 0 0 0 0 0 51 ]
The recent dissertation by Peter Krulevitch (1994, Mechanical Engineering, U.C.
Berkeley) discusses the issues of material modeling for various problems. It
may be of some help in sorting this out.
I hope this helps!
George C. Johnson
Department of Mechanical Engineering
University of California
Berkeley, CA 94720-1740
510-642-3371 (phone)
510-642-6163 (fax)
gjohnson@me.berkeley.edu