34. A. Mundl et al., Science 356, 66–69 (2017).
35. B. S. A. Schuberth, H.-P. Bunge, J. Ritsema, Geochem.
Geophys. Geosyst. 10, Q05W03 (2009).
36. P. Koelemeijer, A. Deuss, J. Ritsema, Nat. Commun. 8, 15241
37. M. Li, A. K. McNamara, E. J. Garnero, Nat. Geosci. 7, 366–370
38. M. D. Ballmer, L. Schumacher, V. Lekic, C. Thomas, G. Ito,
Geochem. Geophys. Geosyst. 17, 5056–5077 (2016).
39. G. Schubert, G. Masters, P. Olson, P. Tackley, Phys. Earth
Planet. Inter. 146, 147–162 (2004).
40. Y. Masson, B. Romanowicz, Geophys. J. Int. 208, 674–692
41. Y. Fukao, M. Obayashi, J. Geophys. Res. 118, 5920–5938
We thank S. Cottaar for introducing us to the 3D modeling
approach used in this study and the IRIS (Incorporated Research
Institutions for Seismology) data center for archiving and providing
all the data. We thank three anonymous reviewers for helping
improve the manuscript. This work was supported by a grant
(EAR-1464014) from the Cooperative Studies of the Earth’s Deep
Interior program of the NSF and an Advanced Grant (WAVETOMO)
from the European Research Council under the European
Commission’s Seventh Framework Programme. K. Y. performed
the data analysis and computations and prepared the figures and
technical details. B.R. provided the intellectual framework and
guidance for the project and wrote the manuscript.
Materials and Methods
Figs. S1 to S13
Tables S1 and S2
3 March 2017; accepted 19 June 2017
Nanocrystalline copper films are
Xiaopu Zhang,1 Jian Han,2 John J. Plombon,3 Adrian P. Sutton,4
David J. Srolovitz,2,5 John J. Boland1*
We used scanning tunneling microscopy to study low-angle grain boundaries at the surface
of nearly planar copper nanocrystalline (111) films. The presence of grain boundaries and
their emergence at the film surface create valleys composed of dissociated edge
dislocations and ridges where partial dislocations have recombined. Geometric analysis
and simulations indicated that valleys and ridges were created by an out-of-plane grain
rotation driven by reduction of grain boundary energy. These results suggest that in
general, it is impossible to form flat two-dimensional nanocrystalline films of copper and
other metals exhibiting small stacking fault energies and/or large elastic anisotropy, which
induce a large anisotropy in the dislocation-line energy.
Nanocrystalline (NC) metals are widely used as electrical contacts and interconnects in ultralarge-scale integrated circuits (1). Tech- nologically important properties of these materials, such as their electrical and ther-
mal conductivity (2, 3), and detrimental processes
such as electromigration (4) are strongly influ-
enced by the presence and density of surfaces,
grain boundaries (GBs), and dislocations within
them. Also, surface roughness of films can affect
materials grown on existing NC films, such as
dielectrics, and will affect the performance of
tunneling devices based on these metals by
modulating the tunnel barrier width (5). Many
NC films contain grains with a preferred ori-
entation; for example, face-centered-cubic (fcc)
metals such as gold and copper (Cu) often grow
with (111) surface orientation (6), so it might be
expected that individual grains and GBs would
coalesce to form films with smooth surfaces. How-
ever, GBs in metals such as Cu are composed of
stacking faults (SFs) whose energies have a di-
rectional dependence that could induce grain
rotation and concomitant surface roughening.
We investigated NC Cu films from the multi-grain scale ~1 mm down to the atomic scale using
scanning tunneling microscopy (STM). We can
use STM to map the local three-dimensional
topography of GB intersections at surfaces with
picometer precision. Also, STM operation is unaffected by the degree of tilt axis misalignment
from high-symmetry directions that typically hampers transmission electron microscopy analysis of
GB structure (7, 8). We identified shifts in the GB
tilt axis away from that of the original low-angle
GB (LAGB) in NC Cu films. We show that this phenomenon is accompanied by GB energy minimization associated with a change in the dislocation-line
direction, which results in the unavoidable introduction of ridges and valleys into the film.
We prepared high-quality NC Cu films (
thick-nesses of 20 or 50 nm) by means of physical vapor
deposition on top of a 7-nm-thick tantalum layer
that had been coated on a silicon wafer (all depositions with the substrate at room temperature).
These samples were etched with glacial acetic acid
and loaded into an ultrahigh vacuum system
1School of Chemistry, Centre for Research on Adaptive
Nanostructures and Nanodevices (CRANN) and Advanced
Materials and Bioengineering Research (AMBER), Trinity College
Dublin, Dublin 2, Ireland. 2Department of Materials Science and
Engineering, University of Pennsylvania, Philadelphia, PA 19104,
USA. 3Components Research, Intel Corporation, Hillsboro, OR
97124, USA. 4Department of Physics, Imperial College London,
Exhibition Road, London SW7 2AZ, UK. 5Department of
Mechanical Engineering and Applied Mechanics, University of
Pennsylvania, Philadelphia, PA 19104, USA.
*Corresponding author. Email: firstname.lastname@example.org
Fig. 1. GBs at ridges and valleys in (111) films of Cu. (A) Perspective
view of the STM topography of NC Cu film. Tunneling parameters are
I = 20 pA and U = 0.2 V. GBs at ridge and valley locations are highlighted
by arrows. (B) Close-up view of one GB at valley location. (C) Close-
up view of one GB at ridge location. (D) Profile of valley and ridge
line cross sections marked by the dashed lines in (B) and (C),
respectively. The color of each curve is consistent with that of lines in
(B) and (C).