Stresses in Cu Thin Films and Ag/Ni Multilayers - Harvard School of ...

Chapter 2: The Elastic Properties of Cu Thin Films 27
Table 2.3: Thermomechanical properties of the substrates used for the thermal cycling
experiments.
Material Ys (GPa) ∗ CTE (10 −6 K −1 ) † Thickness (µm) Ref.
Si(001) 180.5 2.708 395 & 97 [249]
Ge(111) 183.4 5.905 461 [188]
α-Al2O3(0001) 608.4 5.313 257 [86], [249]
fused silica 86.5 0.52 162 [203]
∗ at 25 ◦ C
† at 40 ◦ C
through the (111) pole figure and are sufficient to describe fiber textures, although a full
ODF eliminates the peak overlap sometimes present in fiber texture plots.
The fiber texture plots were performed on the diffractometer shown in Figure 1.5. As
discussed by Wcislak et al. [241], using a linear position sensitive detector to find the
integrated intensity of the peak as a function of χ eliminates most of the corrections needed
with a point detector [126, 135], but the thin film absorption correction (Appendix B) is still
required. The volume fraction of 〈hkl〉-oriented grains is given by Baker et al. [10]:
where I 111
hkl
fhkl =
� χmax
0
� χmax
0
I 111
hkl sin χ dχ
I 111
total
sin χ dχ
(2.5)
is the scattered intensity from the 〈hkl〉-oriented grains in the (111) texture plot.
2.3.4 Curvature Measurements
The wafer curvature apparatus used in these experiments was described in Chapter
1, and the curvatures were converted to stresses using the Stoney equation (1.16). The
thermomechanical properties of the various substrates used are listed in Table 2.3.
The films were typically heated and cooled at approximately 5 ◦ C/min in a forming gas
environment. For the elastic thermal cycles, the heating and cooling rate was varied from