strain effects in thin film / si substrates revealed by x-ray ... - ICDD

Copyright ©JCPDS - International Centre for Diffraction Data 2004, Advances in X-ray Analysis, Volume 47. 363
STRAIN EFFECTS IN THIN FILM / Si SUBSTRATES REVEALED BY
X-RAY MICRODIFFRACTION
C.E. Murray 1 , I.C. Noyan 1 , B. Lai 2 , Z. Cai 2
1 IBM T.J. Watson Research Center, Yorktown Heights, NY 10598
2 Avanced Photon Source, Argonne National Laboratory, Argonne, IL 60439
ABSTRACT
The local variation in strain and rotation of the Si substrate due to overlying Ni thin film features
has been observed using X-ray microdiffraction. Residual tensile stress in 1 µm thick, 190 µm
diameter Ni dots of 990 MPa imparted an average compressive stress in the underlying Si
substrate. Ni Kα fluorescence scans, acquired simultaneously with Si (333) diffraction data,
allow for a precise determination of the Ni feature edge location relative to the observed shift in
Si (333) peak position. Rocking curve mesh scans, in which the sample was translated
perpendicular and parallel to the diffraction plane, were used to deconvolute the effects of
substrate strain due to d-spacing shifts and rotation of the local Si surface. In addition, shear
strains at the dot edge imparted a significant shift in the Si (333) diffraction peak, producing a
secondary diffraction peak in modified reciprocal space scans.
INTRODUCTION
The experimental determination of strain distributions in microelectronic devices is an area of
great interest due to the effects of strain on the operational characteristics and reliability of ultralarge
scale interconnect (ULSI) structures. The interaction between deformation fields arising
from metallization features that are transferred to the surrounding dielectric levels and Si
substrate is of critical importance. The most common description of the strain transfer within the
thin film / substrate system involves the Timoshenko formulation (1925), of which Stoney’s
equation is a special case [1]. However, this model is only appropriate in the case of very large,
thin film features. At length scales appropriate to semiconductor metallization (< 100 µm),
effects due to free edges in thin film features play a greater role in governing the strain transfer
between the features and substrate. By using X-ray microdiffraction, we can map the
deformation fields to reveal the type of deformation (dilatation vs. rotation) induced in the
substrate and its extent.
EXPERIMENTAL
190 µm diameter Ni dots of 1 µm thickness were evaporated onto 1” Si (111) substrates at room
temperature and a base pressure of 1.3 x 10 -6 Torr. Si (111) wafers were chosen so that the inplane
elastic modulus in the substrate was isotropic. Characterization of the Ni dots included
both plan-view and cross-sectional measurements. The mass contrast in the FIB, as seen in
Figure 1a, revealed a ‘halo’ of Ni extending approximately 30 µm from the dot edge due to
shadowing effects from the deposition mask. To determine the variation in Ni thickness, cross-

Copyright ©JCPDS - International Centre for Diffraction Data 2004, Advances in X-ray Analysis, Volume 47. 364
sectional TEM samples were prepared from a section near the dot edge. The cross-sectional
TEM view in Figure 1b illustrates the small grain size of the Ni dot and the profile of the dot
height, which spans from approximately 1 µm through the majority of the dot to 40 nm in the
halo region. Although the Ni thickness in the halo region was too small to induce stress in the Si
substrate, its presence reduced the X-ray diffracted intensity from the substrate due to absorption.
a)
b)
Ni
Si
Figure 1: a) Secondary electron image of a Ni dot deposited on Si (111) substrate. b) Crosssectional
TEM image near the Ni dot edge of the Ni dot / Si substrate sample. Note that a
protective Pt layer was deposited over the region of interest prior to TEM sample fabrication.
Measurements were conducted at the Advanced Photon Source at Argonne National Laboratory.
The hard X-ray microdiffraction apparatus at the 2ID-D beamline was used for the
measurements [2]. A single crystal monochromator was employed to produce a beam with
energy 8.5 keV and zone plate optics were used to focus the beam to a nominal spot size of
approximately 0.3 µm. A vertical kappa diffractometer was used in which a Si (001) analyzer
crystal was placed between the sample and the Bicron detector to reduce the beam divergence.
An X-ray fluorescence detector was used so that X-ray diffraction and fluorescence could be
simultaneously measured. The Ni Kα fluorescence was monitored so that the beam location
with respect to the thin film feature was known at all times. Rocking curves were obtained as the
beam location translated across the Ni dot to produce a map of Si (333) intensity as a function of
position. Maps of Si (333) intensity were collected as both the angle of the sample (θ) and the
detector (2θ) were varied to produce modified reciprocal space mesh scans at selected positions
near and inside the Ni dot edges.
RESULTS
Areal scans of Si (333) rocking curves vs. sample translation were obtained by varying the beam
position in one of two perpendicular directions. The first geometry, as illustrated in Figure 2a,
involved moving the sample in a direction normal to the diffraction plane, that which contains
the incident X-ray beam (S 0 ) and the diffraction vector (k). Si (333) diffracted intensity was
collected from rocking curves as a function of position. To quantify the shift in Si (333) peak

Copyright ©JCPDS - International Centre for Diffraction Data 2004, Advances in X-ray Analysis, Volume 47. 365
a) b)
Diffraction
plane
45.782
45.780
Si
Ni
k
S 0
θ fit [deg]
45.778
45.776
Scanning
direction
45.774
45.772
-200 -100 0 100 200
Distance from dot center [µm]
Figure 2: a) Diffraction geometry used to collect rocking curves of the Si (333) intensity across
the Ni dot feature. Scanning direction was normal to the diffraction plane, defined by the
incident X-ray beam (S 0 ) and the diffraction vector (k). b) Fitted Si (333) peak center vs.
position across Ni dot.
position as the beam traversed the Ni dot, diffraction profiles from each of the rocking curves
were fit to Gaussian curves. The fitted peak centers are plotted in Figure 2b as a function of
position from the dot center. The shift in peak position is symmetric with respect to the dot
center, indicating that the shift is due to the change in d-spacing in the Si lattice. Any effects due
to the rotation of the Si lattice should tilt the diffraction vector out of the diffraction plane,
depicted in Figure 2a, and would not be captured in diffraction information obtained from scans
in which the rocking angle axis is normal to the diffraction plane.
a) Diffraction
b)
plane
k
Si
Ni
S 0
∆θ fit [deg]
0.006
0.004
0.002
0.000
-0.002
Scanning
direction
-0.004
-0.006
-200 -100 0 100 200
Distance from dot center [µm]
Figure 3: a) Additional diffraction geometry used to collect rocking curves of the Si (333)
intensity. Scanning direction was parallel to the diffraction plane. b) Shift in Si (333) peak
center vs. position after deconvoluting the shift due to d-spacing change in Figure 2b.

Copyright ©JCPDS - International Centre for Diffraction Data 2004, Advances in X-ray Analysis, Volume 47. 366
In contrast, the geometry illustrated in Figure 3a, in which the direction of the sample motion is
parallel to the diffraction plane, produced Si (333) diffracted intensity profiles that are no longer
symmetric with respect to the Ni dot center. The rocking curves obtained using this geometry
captured the effects due to the shift in d-spacing as well as the rotation of the Si lattice vector. In
order to extract the Si lattice rotation information, it was necessary to first deconvolute the peak
shift due to the change in d-spacing, shown in Figure 2b. The resulting distribution of the shift in
the peak centers, plotted in Figure 3b, corresponds to an antisymmetric distribution of Si lattice
orientation with respect to the dot center.
a)
b)
+θ
Ni
Si
+ θ
- θ
Figure 4: a) Schematic depiction of the rotation of Si surface lattice vectors due to overlying Ni
dot in tension and b) expected shift in θ position of the Si (333) peak from the substrate normal.
X-ray d vs. sin 2 (ψ) analysis revealed that the Ni dots were under approximately 990 MPa of
tensile stress. Elastic theory for the bending of plates [3] prescribes that the Si substrate
underneath the dot would be in a state of compression where the Si lattice planes would be
rotated inward towards the dot center, schematically drawn in Figure 4a. As the position of the
2θ
θ
Si
Ni
Figure 5: Modified reciprocal space mesh scans (θ vs. 2θ) in the bare Si, away from the effects
of the overlying Ni dot, and those near the Ni dot edge.

Copyright ©JCPDS - International Centre for Diffraction Data 2004, Advances in X-ray Analysis, Volume 47. 367
beam moves across the sample, the tilt angle (θ) needed to rock the diffracted beam into the
Bragg condition is depicted in Figure 4b. This figure corresponds well to the measured peak
shift distribution from Figure 3b and is consistent with the Si lattice vectors being tilted inwards
toward the dot center.
Figure 5 contains modified reciprocal space scans of Si (333) intensity contains the Si (333)
diffracted intensity as a function of θ and 2θ at 3 locations from the Si substrate. The left-most
scan, which is taken from the bare Si surface, displays the footprint of the beam as a single strip
with two maxima due to the beam stop. A secondary strip of diffracted intensity appears in the
Si (333) modified reciprocal space mesh scans near the dot edge and underneath the dot where
the shear strain is maximized. Because Pendellösung fringes appeared between the primary and
secondary diffraction peaks, it is believed that the effects of lattice tilt are being observed from
dynamical diffraction effects between the Si lattice planes near the Ni dot and those deeper in the
substrate. This effect is currently being investigated using dynamic diffraction simulations in
which a strain gradient through the substrate thickness is present.
SUMMARY
The effects of strain in Si substrates due to overlying thin film features can be detected using X-
ray microdiffraction. By analyzing both the diffracted peak position and integrated intensity, one
can determine the extent and magnitude of the strain fields. The variation in peak position
details the rotation and d-spacing shift in the Si lattice due to kinematic diffraction effects. The
shift in peak position is most pronounced underneath the Ni dot edges. Rocking curve mesh
scans in which the sample was translated perpendicular to the diffraction plane were used to
deconvolute the effects of substrate strain due to d-spacing shifts. The rocking curve mesh scans
obtained parallel to the diffraction plane reveal an antisymmetric profile in the shift of peak
position across the Ni dot in which the local Si surface normal vectors are tilted inward towards
the dot center. These results are consistent with the predicted behavior in the Si surface from
beam and plate bending theory given an overlying Ni dot in tension.
ACKNOWLEDGMENTS
The authors would like to thank S.J. Chey for sample fabrication, C.C. Goldsmith for the X-ray
stress measurements and H. Yan for dynamical diffraction work. Work at the Advanced Photon
Source was supported by the U.S. Dept. of Energy, Office of Science, Basic Energy Sciences,
under Contract No. W-31-109-Eng-38.
REFERENCES
[1] S. Timoshenko, J. Opt. Soc. Am. 11, 233 (1925)
[2] J. Libera, Z. Cai, B. Lai and S. Xu, Rev. Sci. Instrum. 73, 1506 (2002)
[3] S. Timoshenko and S. Woinosky-Krieger, Theory of Plates and Shells, 2 nd Ed. (McGraw-
Hill, New York, 1959)