Controllable deformation of silicon nanowires with strain up to 24%

Abstract

Fabricated silicon nanostructures demonstrate mechanical properties unlike their macroscopic counterparts. Here we use a force mediating polymer to controllably and reversibly deform silicon nanowires. This technique is demonstrated on multiple nanowire configurations, which undergo deformation without noticeable macroscopic damage after the polymer is removed. Calculations estimate a maximum of nearly 24% strain induced in 30 nm diameter pillars. The use of an electron activated polymer allows retention of the strained configuration without any external input. As a further illustration of this technique, we demonstrate nanoscale tweezing by capturing 300 nm alumina beads using circular arrays of these silicon nanowires.

Full text

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Controllable deformation of silicon nanowires with strain up to 24%
Sameer S. Walavalkar,a?Andrew P. Homyk, M. David Henry, and Axel Scherer
Department of Applied Physics, Kavli Nanoscience Institute, Caltech, 1200 E. California Blvd, Pasadena,
California 91125, USA
?Received 16 February 2010; accepted 26 April 2010; published online 22 June 2010?
Fabricated silicon nanostructures demonstrate mechanical properties unlike their macroscopic
counterparts. Here we use a force mediating polymer to controllably and reversibly deform silicon
nanowires. This technique is demonstrated on multiple nanowire configurations, which undergo
deformation without noticeable macroscopic damage after the polymer is removed. Calculations
estimate a maximum of nearly 24% strain induced in 30 nm diameter pillars. The use of an electron
activated polymer allows retention of the strained configuration without any external input. As a
further illustration of this technique, we demonstrate nanoscale tweezing by capturing 300 nm
alumina beads using circular arrays of these silicon nanowires. © 2010 American Institute of
Physics. ?doi:10.1063/1.3436589?
I. INTRODUCTION
Designing, etching, and manipulating silicon nanowires
has become increasingly important to a variety of research
areasincludingnanoelectromechanical
optics/plasmonics,1and nanoscale circuit elements. Specific
applications include high surface area chemical sensors,2me-
chanical oscillators,3,4and piezoresistive sensors. High as-
pect ratio pillars with diameters between 50–100 nm could
prove useful for core-shell type plasmonic resonators,5while
pillars with sub-10 nm diameters have shown promising light
emission characteristics.6,7High aspect ratio structures also
have possible applications to high density electronics such as
FinFETS ?Ref. 3? or in DRAM devices.
Current fabrication and manipulation techniques suffer
from a few limitations. For applications requiring precision
placement of pillars, including electronics and optical cou-
pling, a top-down fabrication scheme is required. However,
even with current electron beam technology, alignment with
accuracy greater than 10 nm is difficult. Mechanical manipu-
lation using electrostatic actuation8,9requires power to be
continuously supplied to the device to maintain deformation.
Other static deformation methods—such as pseudomorphic
growth—lack the ability to reversibly tune the amount of
strain in the pillars once they have been patterned, and can-
not achieve strain ?2–3%.10,11Given its influence on elec-
tronic as well as optical properties,11–13methods to accu-
rately control strain are becoming increasingly important in
modern devices.
Previous work has shown that nanoscale structures ex-
periencedeformation differently
counterparts.14–19Specifically silicon nanowires can demon-
strate yeild strength as well as total strain much greater than
bulk silicon.20,21In two notable studies21,22grown silicon
nanowires were shown to have an elongation ratio of 125%
and a maximum strain of 21.5% without failure. Furthermore
previous efforts have utilized the length contraction of poly-
merization to apply significant forces to induce elongation,
systems,
than theirbulk
buckling, and bending of silicon nanowires and carbon
nanotubes.21–23However, common limitations shared by
these approaches are the use of grown nanowires or nano-
tubes resulting in stochastically distributed structures21,23as
well as the permanence of the deformed position achieved by
the nanowire or nanotube.
Here we present a novel method of passively manipulat-
ing etched silicon nanowires using polymethyl-methacrylate
?PMMA? as a force mediating polymer. The force exerted by
the PMMA on the nanowires may be tuned by varying the
electron beam exposure, heating, and selective polymer re-
moval, permitting controllable, as well as fully reversible,
bending and straining of structures. Due to the stability of
PMMA at room temperature, the nanowire configuration re-
mains fixed, enabling further electrical or mechanical tests to
be performed on the sample while under strain. This paper
details the nanowire fabrication, polymer manipulation, de-
formation characteristics, and sample applications of this
technique.
II. METHODS
The fabrication of the nanowires follows Henry et al.24
pillars were defined by e-beam patterning an array of 30–150
nm disks in 75 nm of Micro-Chem PMMA 950 A2. A 25 nm
layer of Al2O3was deposited as a hard-mask via dc magne-
tron sputtering of aluminum with a 5:1 Ar:O2process chem-
istry and patterned via lift-off. Aluminum oxide has been
demonstrated as a resilient as well as chemically inert etch
mask24providing a selectivity of greater than 60:1 for a fluo-
rine etch chemistry. Etching was performed in an Oxford
Plasmalab 100 ICP-RIE 380 machine running a “Pseudo
Bosch” etch with simultaneous etching using SF6and passi-
vation using C4F8—so-called mixed-mode etching. Sidewall
profiles are controlled by adjusting the ratio of etch to pas-
sivation gases. If diameter reduction was required, pillars
were thermally oxidized down to a desired width and then
dipped in buffered hydrofluoric acid to remove the oxide. An
example of a fabricated nanowire array is given in Fig. 1.
a?Electronic mail: walavalk@caltech.edu.
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To prepare the sample for actuation, PMMA is spun over
the pillar area and baked to drive off solvents. The PMMA is
then planarized using an oxygen plasma to achieve the de-
sired resist height.
It has been noted25,26that under high electron beam
doses—approximately ten times the standard dose used in
electron beam lithography—the normally positive-tone
PMMA crosslinks and behaves as a negative resist. Along
with this change in resist tone, the crosslinking causes a
volumetric contraction of the resist. We utilize this contrac-
tion to selectively deform pillars; directional control is
achieved using asymmetric electron beam exposure.
Figure 2 shows two sets of 75 nm diameter nanowires
emerging from a 300 nm thick PMMA film. By exposing
only the right set of pillars, crosslinking in this area pulls
these pillars inwards while neighboring strips remain unde-
formed. The inset shows the comparison in more detail. We
note that the bottom few pillars of both the right and left
patterns have been brought together from the exposure of
taking this picture. The length of exposure dictates the elec-
tron dose and hence the amount of contraction between pil-
lars. Since this exposure is done in an Scanning Electron
Microscope ?SEM?, we could view the progress of the defor-
mation in real time, freeze exposures, take measurements,
and continue until a desired exposure was obtained. Using
this process, it should be possible to obtain SEM resolution
limited precision in the final positioning of the pillars.
In a second experiment, we arranged rings of eight nano-
wires 75 nm in diameter and 800 nm tall ?Fig. 3?. The rings
were initially 500 nm in diameter with 230 nm circumferen-
tial spacing between the pillars. The central region of the
ring was exposed in an SEM, yielding a uniform radial de-
formation. Contraction terminated when the pillars were
flush, with a final diameter of 184 nm after exposure. As
shown in Fig. 4, we also exposed the inner region of a ring of
50 nm diameter pillars that were 1 ?m tall. The ring started
at 500 nm in diameter and contracted until the pillars were
fully touching, giving a deformation distance at the tip of
approximately 250 nm. By measuring the beam current and
exposure time, we determined that a dose of approximately
10 000 ?C/cm2is required to achieve full contraction of the
pillars. This dose matches other results for that required to
fully-crosslink PMMA.26
An interesting consequence of overexposing the resist is
its resilience to dissolution by acetone.25,26Once the area of
interest had been exposed, we dipped the sample in acetone
to remove the nonoverexposed portions of resist, leaving the
intended pillars locked in place while freeing the rest of the
chip from PMMA. This permits further processing steps to
be performed on the chip. Pillars can be relaxed by heating
the chip, causing the PMMA to reflow, or by removing the
FIG. 1. An array of pillars fabricated via conventional top down CMOS
processing. The pillars are 50 nm wide and 1.3 microns tall. The image is
taken at 30°.
FIG. 2. ?a? SEM of deformed strip next to an undeformed strip. ?b? Closeup
of lower section of deformed strip of pillars. Note the increased bend angle
for the pillars that were originally further apart. Scale bar in inset is one
micron.
FIG. 3. ?a? Array of 75 nm pillars in circular patterns with 500 nm diameter
spacing. ?b? Contraction of pillars after the exposure of the central region.
Scale bar is 500 nm.
FIG. 4. ?a? 500 nm wide circle of 50 nm diameter pillars, ?b? same array
after deformation, ?c? same array after oxygen plasma release. Scale bar in
picture is 1 micron.
124314-2 Walavalkar et al.J. Appl. Phys. 107, 124314 ?2010?
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Page 3

PMMA with an oxygen plasma ?inset, Fig. 4?. After a plasma
clean it was possible to repeat the process of straining and
unstraining the pillars. This cyclic loading without fracture
has been previously demonstrated in amorphous silicon
samples.27
For illustration of the extent of possible bending a seg-
ment of polymer was attached to the entirety of a set of
pillars and contracted with an electron beam ?Fig. 5?a??. Fig-
ure 5?b? shows the near-horizontal bending of the pillar un-
der full contraction. Finally, Fig. 5?c? highlights two pillars
that have returned to their original configuration after partial
polymer removal via electron beam ablation. It is important
to note that the pillars still held in their bent configuration in
frame c are held in place by still present strands of polymer.
III. RESULTS AND DISCUSSION
An application of this procedure is the ability to predict-
ably incorporate enormous amounts of strain into nanostruc-
tures. In order to estimate the strain induced in the pillars, we
analyze the structure in a manner similar to Timoshenko’s
treatment of a bimetallic strip.28The actual geometry and
material characteristics of the crosslinked region are difficult
to measure and likely nonuniform, in reality behaving as a
distributed film rather than an isolated region with clear
boundaries. Additionally, the system could be complicated
by slip at the interface, nonlinear elastic behavior of the
polymer, and increasingly surface-dominated mechanical
characteristics at the nanoscale. In spite of the simplified
model, however, the proposed treatment shows excellent
agreement with experimental data. Furthermore, the analysis
predicts a constant radius-of-curvature, yielding a conserva-
tive estimate of the maximum strain.
We model the pillar as a cylinder with diameter d, and
approximate the crosslinked region of PMMA which contrib-
utes to the deformation as a semicircular shell around the
pillar with radial thickness t and originally spun to a film
thickness L ?Fig. 6?a??. After exposure, an equivalent, free-
standing crosslinked region would undergo a uniform verti-
cal contraction by an amount ?L, corresponding to a unit
contraction ???L/L. The length mismatch between the
submerged portion of the pillar and the contracted PMMA
causes the pillar to bend to an angle ? relative to the original
pillar axis and substrate normal.
Following Timoshenko, we find:
1
?=
??Cp− Cs?
EsIs
EpAp
Is
As
+Ip
Ap
++EpIp
EsAs
+ ?Cp− Cs?2
,
?1?
where ? is the radius of curvature, ???L/L is the unit con-
traction of the PMMA, Cp,Csdenote the center-of-mass co-
ordinates, Ip,Isthe cross-sectional moments, Ap,Asthe areas,
FIG. 5. ?a? Clump of polymer stuck to top of pillars begins to bend the
array, ?b? same array after full deformation, ?c? same array after polymer has
been partially removed. Note the highlighted pillars have snapped back up-
right. Also note that the still bent pillars are held in place by strands of
polymer. Scale bars are 250 nm.
0 204060
Pillar Diameter (nm)
80100120140
0
20
40
60
80
Bend Angle (°)
Bend Angle vs. Pillar Diameter
75nm PMMA
150nm PMMA
300nm PMMA
b)
a)
0204060
Pillar Diameter (nm)
80100120 140
0
5
10
15
20
25
Strain (%)
Strain vs. Pillar Diameter
75nm PMMA
150nm PMMA
300nm PMMA
c)
FIG. 6. ?Color online? ?a? Diagram illustrating the theoretical model. A
small, semicircular region of PMMA adjacent to a silicon pillar undergoes
vertical contraction due to electron-beam-induced crosslinking, yielding
large pillar deformation. In the experiment, the crosslinked region is con-
trolled by asymmetric electron-beam exposure, and is embedded in a con-
tinuous polymer film. ?b? Variation in the maximum deformation angle with
the diameter of the pillars, for various resist thicknesses. Theoretical model
is independent of resist thickness. ?c? Variation in the estimated strain in the
pillars with the diameter of the pillars, for varying resist thicknesses. Points
represent averages over several measurements, with error bars indicating the
standard deviations.
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Page 4

and Ep,Esthe Young’s moduli for the PMMA and silicon,
respectively. The arclength along the neutral axis remains at
the original polymer thickness L, yielding an exit angle ?
=L/?
? =
L??Cp− Cs?
EsIs
EpAp
Is
As
+Ip
Ap
++EpIp
EsAs
+ ?Cp− Cs?2
.
?2?
For the geometry described above and a coordinate system
where x=0 corresponds to the center of the pillar, we have
Cs= 0
Cp=3d2+ 6dt + 4t2
3??d + t?
,
As=?d2
4
Ap=?t?d + t?
2
,
Is=?d4
64
Ip= Ap?d2+ 2dt + 2t2
8
− Cp
2?.
Taking Es=160 GPa and Ep?5 GPa as the Young’s
modulus for the overexposed PMMA,26we solve for the re-
maining free parameters using a least-squares fit between the
measured pillar angles and our analytic expression for ?,
obtaining ?L?43 nm and t?46 nm. This contraction is on
the order of the vertical contraction in overexposed PMMA
reported elsewhere.26While not measured directly, we esti-
mate the total load applied to the pillars to be on the order of
10 ?N by finite element simulations.
The results are shown in Fig. 6?b?, which illustrates
close agreement between the experimental and analytical
bend angles. It should be noted that although the wires are
approximately a micron in length the entire strained region is
concentrated within the PMMA layer resulting in a large ob-
served bend angle as the pillar leaves the PMMA. Interest-
ingly, the bend angle data does not show any measurable
dependence on resist thickness. In the analytic expression,
this corresponds to a fixed ?L rather than a fixed unit con-
traction ??? as one might expect. The exact cause of this
behavior is unclear and requires further study, but might in-
dicate that the deformation is occurring over a length which
is smaller than the total film thickness. If this is the case, the
strain required to accomplish the same deformation over a
reduced distance would be higher than that estimated below.
Were this distance also fixed, the strain curves would be
independent of the PMMA starting thickness.
To provide a conservative strain estimate, we assume for
now that the deformation is uniform and occurs over the
entire submerged length of the pillar; we note that the portion
of the pillar which extends beyond the PMMA remains un-
strained. Using ????/? for the strain, we find the maxi-
mum strain along the edge of the pillar
? =
?L?Cp− Cs??Cn− Ce?
+Ip
Ap
EpAp
L?Is
As
+
EsIs
+EpIp
EsAs
+ ?Cp− Cs?2?
,
?3?
where ??=Cn−Ceis the distance between the neutral axis
?Cn? and the far edge of the pillar ?Ce?
Cn=EsAsCs+ EpApCp
EsAs+ EpAp
Ce= −d
2.
The results are plotted in Fig. 6?c?, and demonstrate that
we can controllably incorporate 23.9% strain in 30 nm diam-
eter single crystal silicon nanowires. The strain profile within
the pillar is anisotropic; based on the location of the neutral
axis, it is possible to introduce both tensile and compressive
strain or solely tensile. For large pillar diameters, the neutral
axis lies inside the pillar, resulting in tensile strain at the
outer edge and compressive strain on the inner. As the diam-
eter decreases, however, the neutral axis moves toward the
PMMA. For Cn?d/2, corresponding to d?17.6 nm, the
strain is tensile throughout the pillar cross section.
It is important to recall that the stress is only applied
within the 75–300 nm of PMMA, resulting in high values of
strain but only in the submerged region of the pillar. Further-
more, these values fall within the range of reported values
for strain in silicon nanowires under fracture-free polymer-
ization incited deformation.21,22Possible mechanisms that
could allow such extreme behavior have been studied
previously14–16and rely on the relatively small volumes of
nanowires resulting in the fabrication of statistically “defect-
free” structures that lack sites for fracture nucleation. Addi-
tionally, the small diameter of the nanowires could possibly
allow for dislocations to be “annealed” out of a structure by
diffusing to the perimeter.21
Unlike these studies,21,22since our deformation only oc-
curred within the PMMA layer while the uncovered region
remained unaffected, it was impossible to perform an in situ
HRTEM on the strained region to atomistically quantify the
deformation as either elastic or plastic. However, to SEM
resolution each pillar appeared to undergo a macroscopically
elastic deformation, returning to its original position after
being freed from the PMMA even after several tens of bend-
ing and unbending cycles.
Anisotropic strain has recently been exploited as a
method for breaking the inversion symmetry in silicon
photonics,12,13introducing a second order nonlinearity. Fur-
thermore, such asymmetrically strained materials can exhibit
interesting optical selection rules11based on the strained
splitting of the degenerate light and heavy hole bands. Pre-
viously proposed methods to introduce strain typically rely
on the deposition of lattice mismatched layers, a method
which can incorporate only a few percent of strain, and
which is fixed at fabrication time.10,11In contrast, the method
present in this work allows for the incorporation of several
tens of percent of strain as well as being fully tunable and
reversible.
Another application presented in this paper is the ability
to monitor the manipulation of pillars in real time via SEM
while capturing an object. Here we used an array of pillars
that had been selectively actuated to capture a 300 nm alu-
minum oxide polishing bead ?Fig. 7?a??. During capture, the
contraction of the pillars squeezed a collection of beads such
that they were forced through the top of the closed pillars
?Fig. 7?b??. Once the pillars had been closed, the resist was
selectively removed and the captured collection of beads re-
mained trapped within the pillars. We expect this technique
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Page 5

to have important biological applications such as capturing
individual cells for further study. Compared to electrically
actuated nanotweezers,8the polymer-controlled nanowires
may be more densely packed, allowing the study of interac-
tions between neighboring traps, and offer the ability to leave
the tweezers closed without any external input.
IV. CONCLUSION
This work demonstrates the use of PMMA as a force
mediating layer which actuates silicon nanowires. Using
standard top-down fabrication to define the pillars, PMMA
was spun on and planarized to make the force mediating
layer. By overexposure in an SEM, selected regions of the
PMMA were crosslinked to actuate the pillars. It was further
demonstrated that this could be reversed by heating or by
removing the PMMA with an oxygen plasma. The deforma-
tion remained fixed after exposure to ambient atmosphere
due to the stability of the overexposed PMMA, and excess
PMMA was stripped to allow further fabrication. Using ar-
rays of nanowires, we trapped alumina spheres, confirming
that the flexible nature of the pillars can be utilized for cap-
turing nanometer scale objects. In addition, this technique
yields reversible strain of 24% in silicon nanowires, which
may potentially exhibit interesting optical and electrical phe-
nomena.
ACKNOWLEDGMENTS
The authors gratefully acknowledge support from the
Defense Advanced Research Projects Agency ?DARPA? un-
der the NACHOS program, Award No. W911NF-07-1-0277,
the University of Arizona and the National Science Founda-
tion under the CIAN program, sponsor number Y502628,
prime Award No. EEC-0812072, and the Kavli Nanoscience
Institute. Andrew Homyk thankfully recognizes support from
the ARCS foundation. David Henry appreciates support from
the John and Fannie Hertz foundation, and we thank Adrian
Chapman for useful discussions. Sameer S. Walavalkar and
Andrew P. Homyk contributed equally to this work.
1A. R. Guichard, D. N. Barsic, S. Sharma, T. I. Kamins, and M. L. Brong-
ersma, Nano Lett. 6, 2140 ?2006?.
2L. Sainiemi, H. Keskinen, M. Aromaa, L. Luosujarvi, K. Grigoras, T.
Kotiaho, J. Makela, and S. Franssila, Nanotechnology 18, 505303 ?2007?.
3D. Scheible and R. Blick, Appl. Phys. Lett. 84, 4632 ?2004?.
4H. Kim, M. Qin, H. Westphall, L. Smith, and R. Blick, Nanotechnology
18, 4 ?2007?.
5L. Lauhon, M. Gudiksen, D. Wang, and C. Lieber, Nature ?London? 420,
57 ?2002?.
6A. Nassiopoulos, S. Grigoropoulos, and D. Papadimitriou, Appl. Phys.
Lett. 69, 2267 ?1996?.
7P. Photopoulos, A. Nassiopoulou, D. Kouvatsos, and A. Travlos, Appl.
Phys. Lett. 76, 3588 ?2000?.
8P. Bøggild, T. Hansen, C. Tanasa, and F. Grey, Nanotechnology 12, 331
?2001?.
9Z. Tang, Y. Xu, G. Li, and N. Aluru, J. Appl. Phys. 97, 114304 ?2005?.
10J. Singh, Electronic and Optoelectronic Properties of Semiconductor
Structures ?Cambridge University Press, Cambridge, 2003?, Chap. 1.4, pp.
26–31.
11P. Hashemi, L. Gomez, J. Hoyt, M. Robertson, and M. Canonico, Appl.
Phys. Lett. 91, 083109 ?2007?.
12R. Jacobsen, K. Andersen, P. Borel, J. Pedersen, L. Frandsen, O. Hansen,
M. Kristensen, A. Lavirnenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri,
and A. Bjarkalev, Nature ?London? 441, 199 ?2006?.
13N. Hon, K. Tsia, D. Solli, and B. Jalali, Appl. Phys. Lett. 94, 091116
?2009?.
14B. Wu, A. Heidelberg, and J. Boland, Nature Mater. 4, 525 ?2005?.
15J. Zhang, Y. Zhao, and B. Palosz, Appl. Phys. Lett. 90, 043112 ?2007?.
16M.-F. Yu, B. S. Files, S. Arepalli, and R. S. Ruoff, Phys. Rev. Lett. 84,
5552 ?2000?.
17E. Wong, P. Sheehan, and C. Lieber, Science 277, 1971 ?1997?.
18X. Han, Y. F. Zhang, K. Zheng, X. N. Zhang, Z. Zhang, Y. J. Hao, X. Y.
Guo, J. Yuan, and Z. L. Wang, Nano Lett. 7, 452 ?2007?.
19J. R. Greer, J.-Y. Kim, and M. J. Burek, Journal of Materials 61, 19
?2009?.
20C.-L. Hsin, W. Mai, Y. Gu, Y. Gao, C.-T. Huang, Y. Liu, L.-J. Chen, and
Z.-L. Wang, Adv. Mater. 20, 3919 ?2008?.
21K. Zheng, X. Han, L. Wang, Y. Zhang, Y. Yue, Y. Qin, X. Zhang, and Z.
Zhang, Nano Lett. 9, 2471 ?2009?.
22X. Han, K. Zheng, Y. Zhang, X. Zhang, Z. Zhang, and Z. L. Wang, Adv.
Mater. 19, 2112 ?2007?.
23O. Lourie, D. M. Cox, and H. D. Wagner, Phys. Rev. Lett. 81, 1638
?1998?.
24M. Henry, S. Walavalkar, A. Homyk, and A. Scherer, Nanotechnology 20,
255305 ?2009?.
25I. Zailer, J. Frost, V. Chabasseur-Molyneux, C. Ford, and M. Pepper,
Semicond. Sci. Technol. 11, 1235 ?1996?.
26W. H. Teh, C.-T. Liang, M. Graham, and C. G. Smith, J. Micro/Nanolith.
MEMS MOEMS 12, 641 ?2003?.
27C. Gaire, D.-X. Ye, T.-M. Lu, G.-C. Wang, and R. C. Picu, J. Mater. Res.
23, 328 ?2008?.
28S. Timoshenko, J. Opt. Soc. Am. 11, 233 ?1925?.
FIG. 7. ?a? 300 nm alumina polishing bead caught by 100 nm pillars. ?b? 75
nm pillars catching a collection of smaller alumina polishing beads. The
scale bar is 500 nm.
124314-5 Walavalkar et al. J. Appl. Phys. 107, 124314 ?2010?
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