EXAMPLE 17: Full.Coupled Diffusion 312 SUPREM-IV.GS – 2D ...

EXAMPLE 8: Shear Stress
This calculates the stress distribution arising from the nitride initial stress.
Stress arising from thermal expansion mismatch would be included by
specifying a different temp2. Be warned that large thermal steps often
bring into play many more complicated phenomena than the simple ther-
mal expansion mismatch analyzed in SUPREM-IV.GS. For instance
breakdown of film adhesion or structural change may occur, but are not
taken into account in the program.
The principal slip system in silicon is in the direction on 111
planes. This corresponds to the xy shear force in the plane of the simula-
tion. The value 3 10 7 is considered by Hu[2] to be the critical shear stress
for slip in silicon. Dislocations found in regions where the shear stress is
larger than that value will move under the stress field of the nitride film.
Therefore when analyzing stress in the substrate, a principal concern is the
extent of the xy equal to 3 10 7 contour.
plot.2 bound x.mi=-2 x.ma=2 y.ma=4 cl=f
select z=Sxy
contour val=-3e7
The contours of xy equal to 3 10 7 in the silicon are shown in Figure 1.
The contour is a double lobe because the shear stress is related to the polar
components of stress through xy = ( rr - ) sin 2 + r cos 2 rr
sin 2 The function sin 2 is at a maximum around 45˚ from the vertical,
and is zero at = 90˚. Both rr and cos 2 change sign moving from left to
right, so that the sign of xy is the same throughout. This means that a dis-
location which is being driven under the mask by the stress field will con-
tinue to move in that direction after passing the mask edge. However as it
passes through the center, the decrease in shear stress may leave it strand-
ed under the mask edge. The figure shows that the area of influence of the
nitride film is many times greater than its thickness, about 2 m horizon-
tally, and 1.5 m vertically.
SUPREM-IV.GS – 2D Process Simulation for Si and GaAs 279