NANO
LETTERS
Phase Transition and Compressibility in
Silicon Nanowires
2008
Vol. 8, No. 9
2891-2895
Yuejian Wang,*,† Jianzhong Zhang,† Ji Wu,‡ Jeffrey L. Coffer,‡ Zhijun Lin,†
Stanislav V. Sinogeikin,§ Wenge Yang,§ and Yusheng Zhao*,†
LANSCE-DiVision, Los Alamos National Laboratory, New Mexico 87545, Department
of Chemistry, Texas Christian UniVersity, Texas 76129, High-Pressure CollaboratiVe
Access Team and Geophysical Laboratory, Carnegie Institution of Washington,
Building 434 E, 9700 South Cass AVenue, Argonne, Illinois 60439
Received June 10, 2008
ABSTRACT
Silicon nanowires (Si NWs), one-dimensional single crystalline, have recently drawn extensive attention, thanks to their robust applications in
electrical and optical devices as well as in the strengthening of diamond/SiC superhard composites. Here, we conducted high-pressure synchrotron
diffraction experiments in a diamond anvil cell to study phase transitions and compressibility of Si NWs. Our results revealed that the onset
pressure for the Si I-II transformation in Si NWs is approximately 2.0 GPa lower than previously determined values for bulk Si, a trend that
is consistent with the analysis of misfit in strain energy. The bulk modulus of Si-I NWs derived from the pressure-volume measurements
is 123 GPa, which is comparable to that of Si-V NWs but 25% larger than the reported values for bulk silicon. The reduced compressibility
in Si NWs indicates that the unique wire-like structure in nanoscale plays vital roles in the elastic behavior of condensed matter.
The mechanical properties and phase stability of nanometersized inorganic materials such as dots, wires, and belts
strongly depend on their grain size, shape, and structure.
High-pressure synchrotron X-ray diffraction demonstrated
that wurtzite ZnS nanobelts have a wide field of structural
stability up to 6.8 GPa, remarkably different from the bulk
and monodisperse spherical nanoparticles which transform
to the sphalerite structure at ambient conditions.1 Under static
compression in a diamond anvil cell, a superhard phase has
been made from carbon nanotubes, which exhibits bulk
modulus and hardness comparable to diamond.2 Recently,
studies showed that yield strength of nano-Ni measured under
triaxial compression is more than three times higher than
that of micrometer-Ni.3 All of these results demonstrate that
nanostructures lead to distinct, usually enhanced, properties
compared with conventional bulk polycrystalline materials.
One-dimensional (1-D) nanocrystalline semiconductor Si
has been under extensive investigation because of its unique
electronic, electric-mechanical, and optical properties associated with their wire-like geometry.4-6 It is known that
electronic properties in nanoscale materials can be strongly
altered because of the reduced mobility of the electron/hole
pairs. These one-dimensional, nanoscale structures are also
expected to offer practical routes for the strengthening of
* Corresponding author. E-mail: wang_yuejian@hotmail.com (Y.W.) and
yzhao@lanl.gov (Y.Z.).
† Los Alamos National Laboratory.
‡ Texas Christian University.
§ Carnegie Institution of Washington.
10.1021/nl8016576 CCC: $40.75
Published on Web 08/23/2008
2008 American Chemical Society
nanostructured composites, functioning in a way similar to
the steel-bar reinforcement of concretes. However, investigations of nanowires or nanorods under high pressure are
almost a virgin field. Application of 1-D structures for
materials strengthening through high-pressure (P)/hightemperature (T) sintering, for example, requires the knowledge of materials’ mechanical properties and phase stability
under the relevant P-T conditions. In this work, we
conducted synchrotron X-ray diffraction experiments to study
high-pressure behavior of Si NWs, with particular focuses
on pressure-induced phase transformations and equation of
state (EOS). The results are compared with those reported
for bulk Si to elucidate the impacts of 1-D nanostructures
on materials’ elastic properties and phase stability.
Si nanowires were prepared using a vapor-liquid-solid
(VLS) synthetic route with sputtered thin Au films as
catalysts, and the experimental setup is shown in Figure 1.
To fabricate Si nanowires, the Si(100) wafer coated with 20
nm thick Au film was loaded into an alumina boat, which
was then placed in the center of a quartz tube reactor heated
by a 6 in. long oven. After 1 h annealing at 600 °C, 30 sccm
(standard cubic centimeters per minute) SiH4 was then
introduced into the system (0.5% in UHP grade He), which
was further diluted with an additional 3000 sccm helium.
The Si nanowire growth was carried out at 600 °C for 10
min. The silane gas flow was then turned off, and the reactor
was cooled down to room temperature naturally. Brown and
fluffy films of Si nanowires were produced on the Si wafer.
Table 1. Transition Pressure, Unit-Cell Parameters, and
Equations of State for Si-I of Different Morphology
Si morphology
bulk
bulk
bulk
bulk
bulk
nanowires
Figure 1. Diagram of the reactor design for fabrication of Si
nanowires.
Figure 2. Microstructural characterization of fabricated Si NWs.
(a) A typical SEM image. Scale bar is 1 µm. (b) EDX spectrum of
Si NWs. Inset: schematic representation of the atomic structure of
phase Si-I. (c) TEM image. (d) Atomic resolution HRTEM image
of Si NWs. Inset: SAED pattern.
Figure 2a shows the morphology of Si NWs obtained from
scanning electron microscopy (SEM), which consists of
interwoven nanowires. Energy-dispersive X-ray analysis
(EDX; Figure 2b) reveals that the nanowires are composed
purely of Si. Typical transmission electron microscopy
(TEM) image (Figure 21c) demonstrates that Si NWs possess
smooth and clean surface with diameters of 60-80 nm and
lengths up to several tens of micrometers. Both selectedarea electron diffraction (SAED) and high resolution TEM
(HRTEM) images (Figure 2d) show that the nanowire is
single-crystal growing along the [111] direction. The lattice
parameters were measured from the HRTEM image (Figure
1d) under ambient condition, which shows an fcc diamond
phase with a0 ) 5.423(2) Å, Vo ) 159.48(9) Å3, and a
volumetric contraction compared with the reported values
2892
transition
pressure
(GPa)
11.3
11.2
11.7
8.5-9.9
lattice
parameter
ao (Å)
5.43
5.435
5.43075
5.4231
Bo
(GPa)
B′
ref
98
98
100
4.24
4.16
3.84
123(5)
4.24
12
13
14
15
16
this
study
122(5)
4.16
for the bulk Si with a0 ) 5.435 or 5.43075 Å (Table 1). In
a previous study, AlN NWs with an average diameter of 45
nm show an expanded unit cell at ambient conditions.7 These
authors attributed such expansion to the specific shape and
morphology of AlN NWs.
In the case of spherical nano materials, previous studies
revealed a volumetric expansion with grain size less than
15 nm8,9 and volumetric contraction with grain size larger
than this critical value.10 The different behaviors in unitcell parameters of NWs can be reconciled if there also exists
a critical diameter for NWs, which is possibly located
between 45 and 60 nm based on the current study on Si NWs
and previous work on AlN NWs. Along this line of
speculation, both the unique 1-D structure and its diameter
size have effects on the unit cell configuration of NWs at
ambient conditions.
The high-pressure synchrotron X-ray diffraction experiments were performed by employing a gasketed diamond
anvil cell at Sector 16-IDB of HPCAT, Advanced Photon
Source (APS) of Argonne National Laboratory. The incident
monochromatic X-ray beam with wavelength of 0.36806 Å
was focused down to 5-10 µm in diameter. The Si NWs
and liquid pressure transmission medium (4:1 methanol/
ethanol) were loaded into a rhenium gasket hole of 130 µm
diameter and ∼45 µm depth. Several ruby crystals and gold
chips were also mounted inside the gasket hole to serve as
internal pressure standards. The use of ruby allowed us to
quickly estimate the pressure and thus to plan the experimental runs. Furthermore, from the comparison between the
Au and ruby measurements, we can determine the pressures
more accurately inside the sample. Our analysis shows that
below 11 GPa the sample pressures measured from ruby and
Au are essentially identical. At higher pressures, we used
Au as pressure marker to determine the sample pressures.
The diffraction data were collected on a MAR345 image
plate, 350.3597 mm away from the sample, and were
integrated and converted to regular two-dimensional (2-D)
patterns using the software package FIT2D.11
Figure 3 shows the XRD patterns of Si NWs under high
pressure up to 41.0 GPa. Si NWs remain stable in Si-I
(diamond-cubic) in the pressure range of 0 to 8. 5 GPa, as
illustrated in Figure 3a. Upon compression to 9.9 GPa, a
new diffraction peak started to emerge, which can be indexed
to the 200 peak of Si-II (β-Sn). With further compression
to 11.4 GPa, the Si-II became the dominant phase, whereas
the peak intensity of Si-I phase weakened significantly, as
Nano Lett., Vol. 8, No. 9, 2008
Figure 3. Selected synchrotron monochromatic X-ray diffraction patterns collected in diamond anvil cell under compression up to 41 GPa.
(a) Patterns collected up to 8.5 GPa, under which Si NWs remain stable in Si-I phase. (b) Patterns showing the sequence of Si I-II-XI-V
phase transformations in the pressure range of 9.9 to 14.3 GPa. The dark blue, dark pink, dark green, and red colors correspond to Si phases
I, II, XI, and V, respectively. (c) Selected diffraction patterns of Si-V over the pressure range of 15.1 to 33.4 GPa. (d) Patterns showing
phase transitions of Si V-VI-VII above the pressure of 33.4 GPa. The red, dark pink, and dark cyan colors indicate the Si phases V, VI,
and VII, respectively.
shown in Figure 3b. The bracketed onset pressure of 8.5-9.9
GPa for the Si-I - Si-II transition is lower than the reported
values of 11.3-11.7 GPa for microcrystalline Si studied
using essentially identical experimental techniques (Table
1). For experiments performed under nonhydrostatic conditions, the stress concentration at grain contacts of polycrystalline materials will typically enhance the transition to lower
pressures. For example, depending on the pressure medium
used in diamond anvil cell experiments, the onset pressure
of the R-ω phase transformation in Ti metal varied from
4.9 GPa (no pressure medium) to 10.5 GPa (argon pressure
medium).17 The pressure medium used in the present
experiment, however, typically allows experiments to be
conducted under hydrostatic conditions up to 13 GPa. In
addition, with increasing pressure, no peak width broadening
was detected in Si NWs at pressures up to 10 GPa, which
Nano Lett., Vol. 8, No. 9, 2008
confirms that the measurements in this pressure range were
indeed conducted under hydrostatic conditions.
For a solid-state phase transformation under high pressure,
the new phase usually has a different density. This misfit
creates elastic stresses around nuclei and also consumes some
energy.18 As a result, the phase transformation cannot start
immediately at the equilibrium phase boundary but only after
some metastable overshoot in pressure, which provides a
sufficiently large driving force to overcome a nucleation
barrier for transformation to occur. The misfit strain energy
can be expressed as ∆G s)3E∆V2/2Fγ, where E is Young’s
modulus, ∆V is the volume change of the phase transformation, γ is Poisson’s ratio, and F is density of the Si-II phase.8
Previous theoretical studies indicated that the Young’s
modulus of Si NWs decreases monotonously with the
diameter size, varying from 150 GPa for microcrystalline
2893
Figure 4. Pressure-volume data measured at room temperature for
Si NWs. Previous data for bulk Si-I is also plotted for direct
comparison. Errors in the volume measurements are smaller than the
size of plotted symbols. The curves represent results of the least-squares
fit using a third-order Birch-Murnaghan equation of state.
Si to 77 GPa for Si NWs with a diameter of 70 nm.19,20
Furthermore, the volume change (19%) during the Si I-II
phase transformation in Si NWs is smaller than that (22%)
in bulk Si.12 For most of the materials, the Poisson’s ratio is
around 1/3; if we presume that density of Si-II is insensitive
to the shape as well as grain/diameter size, the misfit strain
energy for the Si I-II transformation in Si NWs would be
smaller than that in bulk Si. This tends to lower the energy
barrier and thus enhance the phase transformation in Si NWs
to a lower pressure. The lower activation energy of dislocation and the larger dislocation velocity as well as the
expanded surface area may be the other factors contributing
to the lower transition pressure in Si NWs.19
At 13.4 GPa, Si-II in Si NWs was transformed to Si-XI
(Figure 3b). A further increase in pressure to 14.3 GPa
resulted in the transformation to the Si-V phase, which was
stable up to 33.4 GPa, as shown in Figure 3c. The Si-V
phase has a simple hexagonal crystal structure (space group
P6/mmm) with lattice parameters of a ) 2.533 Å and c )
2.399 Å, and a c/a ratio of 0.947 at 15.1 GPa. The observed
onset pressure of the Si XI-V phase transformation, 14.3
GPa, is comparable to the reported value of 15.4 for bulk
Si.14 This suggests that under high pressure NWs would
gradually lose their nanoscale, wire-like structure and
therefore their effect on the material’s behavior. Upon further
compression, as illustrated in Figure 3d, Si-VI and Si-VII
phases were observed simultaneously at two experimental
pressures of 37.7 and 41.0 GPa. Also, the observed pressures
for the Si-V to Si-VI/VII transformation are comparable
to those observed for the bulk Si. This again demonstrates a
diminishing distinction between NWs and bulk crystalline
Si and provides evidence of a pressure-induced collapse of
wire-like structure under a certain high pressure.
A third-order Birch-Murnaghan equation of state (EOS)21
was used to derive EOS parameters from the measured
pressure-volume data, as shown in Figure 4. Because of
2894
the very limited stability fields for phases II, VI, VII, and
XI, we only derive the bulk modulus (B0) for phases I and
V, which are stable in relatively large pressure ranges (Figure
4). With the pressure derivative of the bulk modulus, B′,
fixed at previously reported values of 4.24 and 4.16, the leastsquares fitting for phase Si-I yields Bo ) 123 ( 5 GPa,
which is approximately 25% larger than the bulk moduli
(98-100 GPa) determined for the phase I of microcrystalline
Si (see also Table 1).12-14 The bulk modulus can be
formulated by Young’s modulus (E) and Poisson’s ratio (γ)
according to the equation: B ) E/{3(1 - 2γ)}. Recently,
Han et al.19 studied the relationship between Young’s
modulus and the diameter of Si NWs and they revealed a
monotonous correlation between these two parameters. Based
on this work, the Young’s modulus corresponding to the
diameter of our Si NWs (∼70 nm) is approximately 77 GPa.
The Poisson ratio of diamond type Si (Si-I) NWs was
reported to be 0.35;22 substitution of these two values into
the above equation results in a bulk modulus value of 128
GPa for Si NWs, which is in good agreement with the present
experimental result. Therefore, both experiments and theoretical calculations reveal a reduced compressibility in Si-I
NWs, indicating that the unique wire-like shape in the
nanoscale plays vital roles in the observed elastic strengthening. Furthermore, the least-squares fitting of our P-V data
yields an ambient unit-cell volume of Vo ) 159.99 ((0.33)
Å3, which is consistent with the value measured from our
TEM study. For Si-V NWs, the least-squares fitting of the
P-V data results in B0 ) 119 (7) GPa, also with B′ fixed at
B′ ) 4.24. Within the experimental uncertainty, this value
is comparable to the bulk modulus of 123 (5) GPa determined
for Si-I. From the same fitting procedure, we obtained Vo
) 14.817 Å3 for Si-V NWs.
In summary, phase transition and bulk modulus of Si NWs
with diameter of 60-80 nm were investigated at pressures
up to 41 GPa under hydrostatic and quasihydrostatic conditions by using synchrotron X-ray diffraction in a diamond
anvil cell. Si NWs exhibit a noticeable volumetric contraction
at ambient conditions. Under high pressure, Si NWs start to
transform to β-Sn structure at a pressure between 8.5 and
9.9 GPa, which is approximately 2 GPa lower than that
observed in the Si microcrystals. This discrepancy can be
explained from the misfit in strain energy, in the sense that
the smaller misfit in Si NWs would stimulate the phase
transformation to a lower pressure. The bulk modulus of Si-I
NWs derived from the P-V measurements is 123 GPa,
which is comparable to that of Si-V NWs but 25% larger
than the reported values for bulk silicon. The reduced
compressibility in Si NWs indicates that the unique wirelike structure in nanoscale plays vital roles in the elastic
behavior of condensed matter.
Acknowledgment. This research is supported by the Los
Alamos National Laboratory, which is operated by Los
Alamos National Security LLC under DOE Contract No. DEAC52-06NA25396. The experimental work was performed
at HPCAT (Sector 16), Advanced Photon Source (APS),
Argonne National Laboratory. HPCAT is supported by DOEBES, DOE-NNSA, NSF, and the W.M. Keck Foundation.
Nano Lett., Vol. 8, No. 9, 2008
APS is supported by DOE-BES, under Contract No. DEAC02-06CH11357, and JLC by the Robert A. Welch
Foundation.
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