Nanoindentation Study of the Mechanical Behavior of
Silicon Nano-springs
Bin Li, Zhiquan Luo and Paul S. Ho
Microelectronics Research Center, University of Texas, Austin, Texas 78712
Toh-Ming Lu
Department of Physics, Rensselaer Polytechnic Institute, Troy, NY 12180
Abstract. This paper presents results of nanoindentation performed on a set of silicon nano-spring samples formed with
glancing angle deposition (GLAD) technique. The load versus displacement curves were recorded to investigate the
mechanical behavior of the nano-spring structures with various column sizes and column spacings. With the
combination of atomic force microscope (AFM) and nanoindentation capabilities, in-situ observation can be carried out
to determine local deformation at the nanometer scale on the sample surface. The mechanical response was found to
depend on the relative dimensions of the tip with respect to the size of the silicon nano-column. The study indicates that
the mechanical behavior of the silicon nano-column can be significantly modified by the optimization of the overall
configuration and dimensions of the silicon springs.
INTRODUCTION
Nanoindentation is commonly used to measure
mechanical properties of thin films and submicron
structures.1"6 In this paper we employed this technique
to investigate the mechanical behavior of silicon nanospring structures. The amorphous silicon nano-springs
were fabricated by GLAD on bare Si substrates and
tungsten plug substrates, respectively.7 It was shown
that the size of the nano-spring depended on the
original size of the initial nucleation site. Thus with
the combination of GLAD and substrate control, nanospring structures with various column sizes and
column spacings can be formed during the deposition.7
Measurements were performed using a Hysitron
Triboscope system with the combined atomic force
microscope (AFM) and nanoindentation capabilities.
AFM is a well-known and reliable method for
characterizing microstructure of sample surface on
nanometer scale. Nanoindentation studies in an AFM
allow local measurements of mechanical properties on
nanometer scale.8"9 With this system, in-situ
observation can be carried out to detect the mechanical
behavior of the single nano-springs. This work of the
nanoindentation on the structured GLAD thin films
provides a fundamental mechanical characterization
for potential micro-cantilevers or resonator devices.
EXPERIMENTAL DETAILS
The samples were prepared by physical vapor
deposition with the GLAD technique as shown in
Fig.I.7"9 The substrate can rotate about both the axis
perpendicular to the plane of the substrate and the axis
parallel to the substrate surface. The incident flux
angle is modified by changing the tilt angle a about
the axis parallel to the substrate surface. In the
deposition, a is 85° and the deposition rate is about
0.45nm/s. The further details of the GLAD technique
can be found in reference [7]. Three nano-spring
samples were formed by the GLAD system in
Rensselaer Polytechnic Institute. One sample was on
bare silicon substrate and the other two samples were
CP683, Characterization and Metrology for VLSI Technology: 2003 International Conference,
edited by D. G. Seiler, A. C. Diebold, T. J. Shaffner, R. McDonald, S. Zollner, R. P. Khosla, and E. M. Secula
© 2003 American Institute of Physics 0-7354-0152-7/03/$20.00
525
TABLE 1. Characteristic Parameters Of The Nano-spring Samples.
Column size (nm)
Column spacing (nm)
Substrate
Sample
-100
Bare Si substrate
A
-70
W plug substrate
-300
B
-800
<100
W plug substrate
-500
C
Column height (|im)
2
2
1.4
FIGURE 2. FIB cross-section image of the nano-spring
structures.
Vapor Srante
(a)
FIGURE 1. Schematic of GLAD technique. Substrate can
rotate around two axis (§ rotation and a rotation)
on tungsten plug substrates. Because the size of the
nano-column depends on the size of initial
nucleation site, nano-springs with different column
size were formed on different substrates as shown in
Table 1. Figure 2 shows a representative Focused ion
beam (FIB) cross-section image of the nano-spring
structures.
The nano-spring structures were observed by AFM
imaging. The measurements were performed at room
temperature in air using a Nanoscope III microscope
(Digital Instrument) with a J scanner at IHz scan
rate.10 The tapping mode images of the sample
surfaces were obtained with a tip of radius less than
lOnm. The nanoindentation measurements were
performed with an add-on force transducer from
Hysitron Inc.. The transducer uses a centrally fixed tip
instead of a bending cantilever to make indents
perpendicular to the sample surface and to record
highly accurate load-displacement curves. In our
experiments a Berkovich indenter was used, which had
an average radius of tip curvature of about 150nm.
Before each indentation, the indentation area was
imaged to ensure that the surface was free of defects or
debris. In order to measure film-only properties
without the influences of substrates, a conservative
rule of thumb is to limit the indentation depth to less
than 10% of the film thickness.6
(c)
FIGURE 3. Tapping mode AFM images of the three nanospring Samples, (a) Sample A, 4x4um2; (b) Sample B,
5x5jim2; (c) Sample C, 5x5}im2
526
RESULTS AND DISCUSSIONS
Fig.3 shows the tapping mode AFM images of the
three Samples. For the bare silicon substrate sample
shown in Fig.3(a), the nano-columns are formed with
an average column diameter of approximately 70nm.
The random arrangement of the columns is due to the
random nucleation at the beginning of deposition. Also
shown on the surface of sample A, some of the
columns are so close-packed as to form clusters. The
average size of clusters is about 200-300nm, and the
average cluster spacing is around 200nm.
FIGURE 4. Load vs. displacement nanoindentation results
for sample A. Segment a-b-c shows the first loadingunloading cycle, and segment c-d-e shows the second cycle.
The loading curve is shown in the inset.
For the nano-springs grown on tungsten plug
substrates, certain regular patterns with different
column sizes were formed as shown in Fig.3(b) and
Fig.3(c), respectively. For sample B shown in Fig.3(b),
the average column thickness is about SOOnm, and the
average column distance is about 300nm. Compared
with sample B, the column density of sample C is
higher than that of sample B, which is shown in
Fig.3(c). The average column thickness of sample C is
around SOOnm, while the average column distance is
less than lOOnm. It also can be estimated from Fig. 3
that the column area packing density of sample C is
about 70%, which is double that of sample B(34%).
Because of the high column area packing density in
sample C, the relative movement of single nano-spring
may be impeded by the interaction among adjacent
springs.
A typical load versus displacement curve of nanospring sample A is shown in Fig.4. The employed
loading curve is shown in the inset. Since the column
size is about 70nm, the indenter with a tip curvature of
150 nm deformed a cluster of spring columns instead
of a single structure. Compared with elastic
deformation, only a small plastic deformation was left
after the unloading process. The contact stiffness of
the spring cluster is about 0.15jiN/nm. Based on the
method shown in reference [1], the modulus of the
spring cluster was calculated to be about IGPa if the
Poisson ratio of the silicon spring is assumed to be 0.3.
The calculated modulus is far less than the modulus of
polysilicon film (170GPa).n This indicates that during
the experiment the elastic behavior is the collective
response of the spring cluster, and the nano-structure is
more compliant than the polysilicon film.
FIGURE 5. Load vs. displacement nanoindentation results
for sample B. (a) Displacement curve of nanoindenation. The
loading curve is shown in the inset. Altogether there are 3
loading cycles. The loading displacement discontinuity is
apparent in the third loading curve, (b) shows displacement
curve of the first two loading cycles, which is cut from (a).
In the displacement curves, segment a-b-c shows the first
loading-unloading cycle, segment c-d-e shows the second
cycle, and segment e-f-g shows the third cycle.
As the column size increases, for example, beyond
the size of the indenter, the mechanical response
reflects the elastic behavior of single silicon spring.
Fig.5 shows the nanoindentation behavior of sample B.
The loading curve is shown in the inset of Fig.5(a),
which includes two loading cycles with lower peak
force and one loading cycle with higher peak force.
From Fig.5 when the applied load was less than
-IluN, a linear response between the displacement
527
polysilicon film. Fig. 7(b) shows that the indenter only
acted on a single silicon nano-column. One possible
reason for this non-spring-like behavior is that the
deformation of the nano-spring may be impeded by
interacting with adjacent springs. The high column
area packing density of sample C (-70%) may result in
an entanglement of nano-columns, which probably
impeded the elastic behavior of the nano-column
structure. The column height of sample C (1400nm)
was smaller than that of sample A and B (2000nm),
which also contributed to the higher stiffness of
sample C.
and the load was observed. There seemed to be no
local plastic deformation of the silicon spring so the
contact area did not change under the low load. The
displacement curves of the first two cycles coincided
with each other quite well. This indicated an elastic
behavior of the single silicon spring below the elastic
limit. From Fig. 5(b) the spring constant of single Si
spring was determined to be 0.2uN/nm.
When the applied force exceeded -IluN, the
displacement increased dramatically with decreasing
the applied force. This can be attributed to the collapse
of the spring structure. For verification, the spring
structure of sample B was imaged by the Berkovich
indenter before and after the nanoindentation
measurement as shown in Fig. 6. The spring structure
indicated by the arrow was probed by the indenter in
the indentation measurement. Fig. 6(b) shows the
image of the same area after nanoindentation. The
spring structure probed by the indenter disappeared
from its original location. This indicated that during a
high load nanoindentation, the indenter may have
collapsed the nano-spring structure instead of slipping
from the spring structure. This can explain the
displacement curve in Fig.5. Although the lateral
resolution of the images in Fig. 6 is lower than that of
the tapping mode images shown in Fig.3 due to the
larger size of the indenter, the nano-spring structure in
Fig. 6 can still be observed.
(a)
(b)
FIGURE 7. Nanoindentation results obtained from sample C.
(a) Typical load-displacement curve for the sample C. The
loading curve is shown in the inset; (b) Surface of sample C
imaged by the Berkovich indenter after nanoindentation
FIGURE 6. Surface of sample B imaged by conventional
AFM mode with the Berkovich indenter. (a) Before
nanoindentation. The indenter acted on the silicon spring
indicated by an arrow; (b) After nanoindentation. The silicon
spring disappeared from the site indicated by the arrow.
Fig. 7 shows the nanoindentation results on sample
C. The displacement curve indicates both elastic and
plastic deformations occurred during indentation. Here
the nano-structure did not behave like a spring under
the applied force. The contact stiffness calculated from
the displacement curve was ~20jiN/nm, which was
about 100 times larger than the single spring constant
of sample B. And the modulus of the nano-structure
was found to be 178GPa, close to the modulus of
CONCLUSION
Nanoindentation
measurements have been
performed on the nano-spring samples with various
column sizes and column spacings. In comparison
with previous studies [8,9], we were able to measure
the mechanical behavior of single nano-spring
structures with a smaller indenter. The mechanical
528
response was found to depend on the size of the
indenter relative to that of the silicon nano-column.
For a small silicon column, the indenter usually
deformed a cluster of spring columns instead of single
structure. With column size approaching the tip radius,
the mechanical response showed an elastic behavior of
a single silicon spring. The spring constant of single Si
spring was determined from the load versus
displacement curve. When the applied force exceeded
elastic limit, the displacement increased dramatically,
due to the collapse of the spring structure. With a
small enough column spacing and a high column area
packing density, the deformation of the nano-spring
seemed to be impeded by interaction with adjacent
springs. Results from this study indicate that the
mechanical response of the silicon nano-spring can be
significantly modified by changing the overall
configuration and dimensions of the silicon springs.
REFERENCES
1. Pharr, G. M., and Oliver, W. C, MRS Bulletin, July 1992,
pp. 28-33.
1. Hodzic, A., Stachurski, Z. H., and Kim, J. K., Polymer
41, 6895-6905(2000).
3. Goken, M., Kempf, M., Bordenet, M., and Vehoff, H.,
Surf. Interface Anal 27, 302-306(1999).
4. Briscoe, B. J., Fiori, L., and Pelillo, E., /. Phys. D: Appl.
Phys. 31, 2395-2405(1998).
5. Gouldstone, A., Koh, H. J., Zeng, K. Y., Giannakopoulos,
A. E., and Suresh, S., Acta mater 48, 2277-2295(2000).
6. Saha, R., and Nix, W. D., Acta mater 50, 23-38(2002).
7. Zhao, Y. P., Ye, D. X., Wang, G. C., and Lu, T. M.,
Nano Letters 2, 351-354(2002).
8. Seto, M. W., Robbie, K., Vick, D., Brett, M. J., and
Kuhn, L., J. Vac. Sci. Technol. B 17, 2172-2177(1999).
9. Seto, M. W., Dick, B., and Brett, M. J., J. Micromech.
Microeng. 11, 582-588(2001).
10. Goken, M., and Kempf, M., Acta mater 47, 10431052(1999).
11. Sharpe, W. N., Yuan, Jr., B., and Vaidyanathan, K. R.,
Proceedings of the Tenth IEEE International Workshop
on Microelectromechanical Systems, Nagoya, Japan,
1997, pp. 424-429.
529