Nanostructures of SingleCrystalSilicon (SCS) with superior electrical, mechanical, thermal, and optical properties are emerging in the development of novel nanodevices. Mechanical properties especially Young's modulus are essential in developing and utilizing such nanodevices. In this paper, experimental researches including bending tests, resonance tests, and tensile tests on Young' s modulus of nanoscaled SCS are reviewed, and their results are compared. It was found that the values of
Being the most important semiconductor used in microelectronics and
microelectromechanical systems, Single Crystalline Silicon (SCS) is still a
research hot spot in nanoscience and nanotechnology, as current trend pushes
sciences and technologies to nanometer scale. Researchers have found that
Being defined as the ratio of tensile stress to tensile
strain,
In this review, we present the recent experimental researches
on Young’s modulus of SCS nanostructures and compare their
Mechanical property measurements of nanostructures, such as nanobeams and nanowires, are very challenging because of the difficulties in (1) sample preparation and nanomanipulating and (2) measuring force and displacement (strain and stress) with nanoscale resolution. But in these years researchers have demonstrated some mechanical tests on SCS nanobeams and nanowires, which cover bending tests, resonance tests, and tensile tests.
Atomic force microscopy (AFM) is usually employed to give 3D
image of the topography of the sample surface, control and apply a specified
amount of force on the sample. It is suitable to use AFM in mechanical tests on
a single- (double-) clamped nanobeam (nanowire) by applying force to the
specimen and measure deformation simultaneously. By using beam bending
equations, the mechanical properties can be deduced. For double-clamped beam
being applied as a force in its middle point, Young’s modulus can be expressed
as
Namazu et al. patterned Si nanobeams by means of
field-enhanced anodization on SOI wafer using AFM and obtained the nanobeams
by anisotropic wet etching, which are <110>-oriented with thickness of
255 nm and widths from 200 to 800 nm. By applying bending tests on these double
clamped nanobeams, the measured values of Young’s modulus are determined to be
169 GPa on average. These results indicate that the specimen size has no
influence on
Virwani et al. patterned some 200–400 nm-wide
Paulo et al. also used AFM to characterize the
mechanical elasticity of their Si nanowires synthesized by Vapor-Liquid-Solid method.
The nanowires are horizontally grown between the two facing Si sidewalls of
microtrenches. The values of
According to Euler-Bernoulli theory, dynamic studies on the resonant frequency of nanobeams and nanowires can provide Young’s modulus when the geometry is determined accurately.
In the work of Li et al. [
(a) Resonant frequency data for a set of
38.5 nm-thick cantilevers (with varied length) are fitted into theoretical curve
based on resonant frequency expression. Young’s modulus of 68 GPa is obtained
from the fitted result. (b) The monotonous decrease in Young’s modulus value of
the ultrathin SCS cantilevers is obtained. The thickness of the cantilevers is
in the range of 300–12 nm. (Reprinted
with permission from [
Among all the methods of
By using a high-resolution TEM equipped inside with
nanomanipulators for sub-nano-Newton force measurements (an AFM) and electronic
conductance measurements (an STM) [
Time-sequent series of high-resolution images
of a tensile deformation process of a single crystalline Si nanowire. The tip of
the cantilever (the left-hand side) is retracted toward the left as indicated
by the bold arrows. (Reprinted with permission from [
Micro-electro-mechanical systems (MEMSs) can be advantageously
employed in the testing of nanoscale samples. It usually consists of three
parts: actuator for nanomanipulating sample, sensor for measuring force on the
sample, and a cofabricated (or later-attached) sample. By integrating MEMS chip in SEM or TEM, researchers have successfully performed several tensile
tests on nanostructures [
We have designed and fabricated an MEMS tensile-testing chip, a
TEM holder with electric terminals, and carried out insitu TEM tensile testing
on SCS nanobeam [
SEM views of the MEMS tensile-testing chip. The
structures of beams and combs are shown. Inset is the enlarged view of the sample, seen through the electron beam window. The <110>-oriented SCS
thin film is connected on its both ends to the supporting structures. (Reprinted
with permission from [
When actuating voltage was applied, with the on-chip comb drive
actuator stretching the SCS nanobeam and insitu TEM observation, tensile tests are performed on the 33
TEM bright field (BF) images of the structures
and the SAD pattern of the SCS nanobeam (inset) TEM images of the movements of
the two ends of the nanobeam,
The experimental results on Young’s modulus of SCS nanobeams
and nanowires are summarized in Table
Experimental results of
Direction | Dimension (nm) | Young’s modulus (GPa) | Testing method | Reference | ||
---|---|---|---|---|---|---|
Nanobeam | Nanowire | |||||
Width | Thickness | diameter | ||||
<110> | 200 | 255 | — | 169 | Bending | [ |
200 | 255 | — | 182 | Bending | [ | |
N.A. | 300 | — | 170 | Resonance | [ | |
N.A. | 170 | — | 135 | Resonance | [ | |
N.A. | 38.5 | — | 68 | Resonance | [ | |
N.A. | 12 | — | 53 | Resonance | [ | |
30000 | 90 | — | 167 | Tensile | [ | |
<100> | 200 | 193 | — | 174 | Bending | [ |
<111> | — | — | 4 | 18 | Tensile | [ |
N.A. | — | — | 120 | 186/207 | Bending | [ |
Values of Young’s modulus versus
nanostructures critical dimension, with
It is also interesting to note that the measured values of Young’s modulus by different testing methods have a little difference. Size effect did not appear at 200 nm-thick nanobeam in bending test, while in resonance test the tendency curve indicates that it should appear at around 250 nm. As for tensile test, Young’s modulus still keeps the bulk value at 90 nm-thick nanobeam.
Compared to the
tensile test result, Young’s modulus by resonance test shows its size effect more early. The different behaviors of
Taking nanobeam,
for instance, a model to explain the difference is constructed, in which the nanobeam
is treated as a composite beam with a silicon middle layer and two surface layers. The difference of Young’s modulus caused by the two different methods can
be described as
Since many theoretical [
Illustration of the different
values of
In this paper, the existing experimental tests of Young’s modulus, including bending tests, resonance tests, and tensile tests, on SCS nanostructures are reviewed. The results suggest that at nanoscale, the silicon Young’s modulus exhibits obvious size effect of a decreasing tendency on the nanostructures decreasing dimension. Different testing methods may give different Young’s modulus values. The size effect of Young’s modulus appears earlier in resonance test than in the other methods. By taking surface effect into account, this difference may be qualitatively explained for SCS nanobeam. It indicates that current experiments are still not enough to understand the behavior of SCS Young’s modulus at nanoscale thoroughly, more research work should be done for it.
This work is partly financially supported by the National Basic Research Program of China Grant no. 2006CB300403 and the Fund for Creative Research of NSFC Grant no. 60721004.