Appl. Phys. Lett., Vol. 76, No. 24, 12 June 2000
Merkulov et al.
3557
lets and subsequent catalytic growth of one VACNF per
droplet. For an initial 15 nm Ni/10 nm Ti dot on Si, the
critical diameter below which only a single VACNF will
grow is ϳ350 nm. Above this critical diameter multiple
VACNFs are formed. VACNF growth along patterned cata-
lyst lines also was demonstrated, and the growth mechanism
is found to be similar, with a critical linewidth of ϳ200 nm
for the same catalyst deposition. We also found that direct
substrate heating during PECVD growth has a significant
advantage in producing large-area growth of VACNFs with
excellent uniformity.
The authors would like to acknowledge and thank I. A.
Merkulov for a stimulating discussion regarding the physical
mechanisms of the cluster formation. They also would like to
thank the SHaRE facility and E. A. Kenik for providing the
XL30/FEG microscope used for the SEM measurements, X.
Fan for preliminary TEM measurements, and P. H. Fleming
for assistance with sample preparation. This research was
partially sponsored by the Defense Advanced Research
Projects Agency under Contract No. DARPA-MIPR-97-
1357 with Oak Ridge National Laboratory ͑ORNL͒ and by
the Office of Basic Energy Sciences, Division of Materials
Sciences, U.S. Department of Energy. The research also was
supported in part by an appointment to the Oak Ridge Na-
tional Laboratory Postdoctoral Research Associates Program
administered jointly by ORNL and the Oak Ridge Institute
for Science and Education and was carried out at ORNL,
managed by Lockheed Martin Energy Research Corp. for the
U.S. Department of Energy, under Contract No. DE-AC05-
96OR22464.
FIG. 3. SEM images taken at 50° tilt ͑a͒ and 0° tilt ͑b͒ showing VACNFs
grown on Ni catalyst lines. ͑a͒ VACNF growth follows the catalyst line
pattern. ͑b͒ The Ni film breaks into little droplets that initiate CNF formation
and then reside on top of VACNFs that grow perpendicular to the substrate.
nanofibers, providing for their continued growth ͓Fig. 3͑b͔͒.
The formation of single or multiple catalyst droplets on a
single patterned catalyst dot can be explained as follows.
As-deposited Ni films have intrinsic tensile stress of ϳ8
ϫ109 dynes/cm2.15 However, upon heating a compressive
stress develops in the films16 due to the different expansion
coefficients for Ni (13ϫ10Ϫ6/°C) and Si (3ϫ10Ϫ6/°C). At
600–700 °C this thermal compressive stress is equal to ϳ2
ϫ1010 dynes/cm2 and thus the net stress will be compressive.
Furthermore, the compressively strained Ni film will develop
propagating sinusoidal wrinkles to minimize the strain
energy.17 This will tend to break large-area films into smaller
patches. However, the wrinkle formation and the subsequent
film breakup increase the surface energy. Consequently, be-
low a critical dot size the breakup does not occur because the
increase in the surface energy would be larger than the re-
duction of the strain energy. Next, at elevated temperatures
the metastable Ni film patches will tend to form clusters to
further reduce the strain energy.18 This results in the
Stranski–Krastanov growth mode: Ni clusters are formed on
top of one or a few monolayers of Ni attached to the sub-
strate surface. The characteristic cluster size will be dictated
by the minimum of the sum of the strain and surface ener-
gies. In the end, large-dot Ni films that break into multiple
patches produce multiple Ni clusters, whereas Ni films on
smaller dots below a critical size form only a single droplet.
The Ti layer, on the other hand, does not form clusters due to
its lower (8.5ϫ10Ϫ6/°C) expansion coefficient ͑lower strain
energy͒ and higher melting point ͑lower mobility of the at-
oms at a given temperature͒.
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