1. Introduction

In the past few decades, nanotechnology has drawn a lot of attention for its novel properties in nanomaterials and dramatic behavior in nanodevices. Nanoscaled structures behave differently from their bulk forms due to their geometries and huge surface-to-volume ratio ^[1-5], which need precise experimental evaluation when used as a functional component in nanodevices. Mechanical property measurements of nanostructures, such as nanobeams and nanowires, are very challenging because of the difficulties in (ⅰ) loading force in control, (ⅱ) measuring force and displacement (strain and stress) at the nanoscale, and (ⅲ) sample preparation and nanomanipulation. However, in recent years, researchers have demonstrated some mechanical tests on nanobeams and nanowires which cover bending tests, resonance tests and tensile tests.

(1) Bending tests: AFM is usually employed to give three-dimensional images 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 the deformation simultaneously. By using beam bending equations, the mechanical properties can be deduced.

(2) Resonance tests: according to the Euler-Bernoulli theory, dynamic studies on the resonant frequency of nanobeams and nanowires can provide Young's modulus when the geometry is determined accurately.

(3) Tensile tests: to facilitate tensile testing on nanostructures, various nanomanipulators, based on multi-axes actuation, were designed to work with SEM or transmission electron microscopy (TEM). With the nanostructure being stretched and tensile force being measured by nanomanipulators, and sample elongation being observed by SEM or TEM, in situ tensile tests are carried out inside the SEM and TEM instruments.

Among all these methods, tensile testing is more challenging because the specimens must be free-standing, clamped at both ends, stretched uniaxially and their elongation measured with nanometer resolution.

MEMS technology gives promising perspectives to produce devices that meet the challenges in tensile testing ^{[6, 7]}, which usually consists of three parts: an actuator for nanomanipulating the sample, a sensor for measuring the force on the sample and a cofabricated (or later-attached) sample. Considering the choosing of actuation technology, generally there are three types of actuators used for performing a tensile test on a nanostructure: piezoelectric ^{[8, 9]}, thermal ^[10-12] and electrostatic ^{[7, 13, 14]}. Compared with the former two types of actuators, the electrostatic actuator has the advantages of being completely compatible with traditional MEMS fabrication technology, a relatively large actuated force, easy attainment of a nearly pure in plane force, and no current generation or heat conduction, which makes electrical measurement on nanosamples very easy to achieve. Therefore, the electrostatic actuator is preferred for electromechanical characterization of the nanosamples in our work. Furthermore, a simplified sensor beam is designed to instead of a traditional capacitive force sensor, which would significantly decrease the complexity of the device and the testing system.

In this paper, we review our study of tensile testing on different nanoscaled materials based on the MEMS electrostatic actuator tensile testing chip.

2. MEMS-based tensile testing electromechanical characterization system^[15]

In order to meet the challenges in tensile testing on nanostructures, as mentioned earlier, a MEMS-based tensile testing electromechanical characterization system in SEM/TEM is proposed as a promising solution. A designed schematic picture of the tensile testing system is shown in Fig. 1(a). A suspended nanosample is fixed on a MEMS electrostatic actuator and a sensor beam, respectively. To provide a controllable, continuous, and uniaxial loading force on the nanosample, the MEMS actuator should be designed carefully. A simplified sensor beam is used to measure the force. When the nanosample is tensiled by the tensile device, the performance of the nanosample can be observed by TEM/SEM directly with nanometer resolution.

Utilizing the tensile device with the nanosample integrated and the designed electromechanical testing system, the nanosample's electronic property and mechanical property can be measured simultaneously, as Figure 1(b) shows. The grey area stands for the electrostatic tensile device, which is placed in the SEM chamber during the experiment. One end of the placed nanowire is connected to the movable combs of the electrostatic actuator, while the other end is connected to a low-stiffness microforce sensor beam, of which the deformation can be measured by SEM imaging and used for evaluating the tensile force applied to the nanowire. Three Au electrodes marked as A, B and C in the tensile device are connected to an $I$-$V$ analyzer and a DC supplier, respectively. The DC supplier is used to apply voltage to the electrostatic actuator, while the $I$-$V$ analyzer is used for resistance measurement of the nanowire.

When voltage was applied to the electrostatic actuator in steps of 3-5 V, with the electrostatic actuator stretching the nanowire, a high-resolution SEM/TEM image of the nanowire and force sensor beam was taken and the $I$-$V$ behavior was measured on the nanowire by the $I$-$V$ analyzer at each step. Elongation of the nanowire can be obtained directly, meanwhile, the force applied on the nanowire can be calculated from the deformation of the sensor beam and the resistance of the nanowire can be calculated from the $I$-$V$ measurements. By these means, in situ SEM/TEM observation and electromechanical characterization of the nanoscaled material were carried out.

The tensile chip was integrated with a comb drive actuator, a force sensor beam and an electron beam window, as schematically shown in Fig. 2. The supporting beams ensured the stretching force to be uniaxial. When the in situ tensile test was carried out, the comb drive actuator pulled the movable structures, the nanosample fixed on the two specimens stretched and the force sensor beam bent. Both the deformation of the nanobeam and the deflection of the sensor beam could be measured through TEM/SEM.

The mechanism of the comb drive actuator is to utilize the tangential electrostatic force of pairs of parallel plates for driving. This force pulls the movable combs to an area that is more overlapping with the fixed combs. The total electrostatic force generated by the actuator can be calculated using the following equation ^[14]:

$\begin{equation} F_{\rm tot}=\frac{n \varepsilon_0 IV^2}{g}, \end{equation}$

(1)

where $n$ is the number of comb pairs, $\varepsilon_0$ is the dielectric constant of free space, $I$ is the height of the comb fingers, $g$ is the gap spacing of the comb fingers, and $V$ is the applied voltage between the movable and fixed combs. Obviously, according to Eq. (1), the higher the voltage applied, the larger the pulling force will be. Both the experimental and theoretical relationships between the actuated voltage and the displacement of the gap spacing of the tensile device are shown in Fig. 3. The experimental result is very close to the theoretical curve, but slightly larger due to the dimensional non-uniformity of the combs after the chip fabricating process. Therefore, a force sensor beam was designed to measure the real tensile force.

The process is shown in Fig. 4. First, a (100) silicon wafer with a thickness of 430 $\mu$m was oxidized, as shown in Fig. 4(a). SiO$_{2}$ was then patterned on both sides and 5 $\mu$m deep trenches were etched by a KOH solution, as shown in Fig. 4(b). Next, another 430 $\mu$m thick wafer was bonded on the top wafer and patterned to reduce the thickness of the corresponding region of the top wafer to 20 $\mu$m, which would eventually be patterned to be a force sensor beam and partial supporting beam, as shown in Fig. 4(c). In Fig. 4(h), SiO$_{2}$ on the top wafer was patterned to be the mask of all functional structures (combs and beams). In Fig. 4(ⅰ), all functional structures such as combs and beams were etched using deep-RIE, followed by removing SiO$_{2}$ on both surfaces using a HF solution. Figure 5 shows an SEM image of an accomplished nanostructure tensile device, from which the force sensor beam, the structure of combs, the Au electrode pads, the hole of the substrate wafer and the gap for integrating nanosamples can be seen clearly. Consequently, a micro-electro-mechanical system tensile testing chip is obtained and an in situ tensile testing system is developed.

3. Sample integrated and nanomanipulated^{[16, 17]}

Besides controlling the loading force and measuring force and the problem of displacement (strain and stress) at the nanoscale, sample preparation and nanomanipulation is another great challenge in tensile testing. In order to obtain an integrated nanoscaled sample on our tensile device, we developed two reliable methods: self-integration in the fabricating processes method and nanomanipulation with the FIB assisted method.

Based on the tensile-testing chip and some modifications of its fabrication process, a suspended SCS nanobeam can be integrated into the chip during the fabricating process, thus making it possible to avoid the challenge of nanomanipulation and preparation of the nanomaterial. The modified process is illustrated in Fig. 6, where the side views are on the left and cross-sectional views on the right. A (100) SOI wafer, with a 200 nm top SCS layer and a 375 nm buried oxide layer, was dry oxidized to reduce the thickness of the top Si layer to 90nm. The non-uniformity of the SCS layer was mainly caused by the non-uniform interface between the SCS layer and the buried oxide layer and was of 5 nm. The wafer was patterned and 10 $\mu$m deep trenches were dry etched to be used as gaps for the movable structures, which were made on the backside. The $\langle$110$\rangle$-oriented nanobeam was also shaped at this step. Another wafer, with a thickness of 400 $\mu$m, was oxidized to a 2$\mu$m SiO$_{2}$ layer, then a though hole was made on it by DRIE to serve as the electron beam window. Bending these two wafers and followed by DRIE and HF etching, all functional structures were shaped and a tensile-testing chip integrated with a suspended SCS beam was achieved, as Figure 7 shows.

Thanks to the development of nanomanipulation technology and FIB technology, various kinds of nanomaterials can be integrated into the tensile device (Fig. 4) ^[18]. As examples, a brief procedure of integrating a copper nanowire into the tensile device is demonstrated in Fig. 8. In general, a nanowire was firstly welded to a tungsten tip using electron beam-induced deposition (EBiD) of platinum (Fig. 8(a)). Then the nanowire was transferred to the tensile device and welded on the Au pads across the gap by EBiD. Before the welding process, receiving trenches were pre-etched on the Au pads by FIB to help aligning the nanowire (Figs. 8(b) and 8(c)). Finally, the nanowire was cut by FIB to separate the tip and the nanowire.

Consequently, by these two means, an SCS nanobeam, a SiC nanowire and a Cu nanowire were properly integrated into our tensile device and the sample preparation was well completed.

4. In situ TEM/SEM electromechanical characterization of nanomaterials using an electrostatic tensile testing device^[15]

4.1 Young's modulus size effect of silicon nanobeam^[19]

With the developed process, four MEMS tensile testing chips integrated with $\langle$100$\rangle$-oriented SCS nanobeams were obtained in a SOI wafer with thicknesses from 45 to 100 nm. Mounting the chips onto a custom-made TEM sample holder, in situ TEM tensile tests were carried out to study Young's modulus at different nanobeam thicknesses.

When the actuating voltage was applied, with the on-chip comb drive actuator stretching the SCS nanobeam and in situ TEM observation, tensile tests were performed on samples. For actuating voltages from 50 to 100 V, incremented in 10 V steps, we took snapshots of the movements of the two ends of the nanobeam, A and B (indicated by the arrows), as shown in Fig. 9. By taking the four corner marks, which were the images of four fixing film clamps in TEM, as reference positions, we measured the displacements of A and B. The elongation of the nanobeam can be obtained from the difference, and the deflection of the force sensor beam can be considered as the displacements of A. The tensile force on the SCS nanobeam was calculated, with the elastic constant of the force sensor beam. By fitting the strain-stress relationship under different actuating voltages, we obtained the Young modulus.

The relationship of Young's modulus ($E$) and the nanobeam thickness ($h$) is presented in Fig. 10; also presented in the figure are the results of resonance tests ^[21], pull-in tests ^[22], and our work ^[20] of tensile tests in SEM. It can be seen that the measured Young modulus (from 74 to 178 GPa) is well in agreement with our previous results of tensile tests in SEM. The measured $E$ decreased monotonically with the decreasing thickness of the SCS nanobeams, which qualitatively matches the relations obtained by resonant tests and pull-in tests. But in resonant/pull-in tests, Young's modulus showed the decreasing tendency earlier compared with the tensile tests. These three sets of Young's moduli appear to approach one value when the nanobeam's thickness approaches approximately 40 nm, and this Young's modulus value is very close to Young's modulus of silicon dioxide.

4.2 Determination of the lattice parameters of a silicon nanobeam^[23]

During uniaxial tensile testing, we can also observe the lattice behavior of an SCS nanobeam. As the electron beam went through the SCS nanobeam, it would be diffracted by the lattice and an SAED pattern would form on the TEM imaging plane. Figure 9 demonstrates both two-dimensional lattice parameters and the SAED pattern of (100) SCS. The relationship between the lattice parameters and the dimensional parameters of the SAED pattern can be deduced from the basic theory of electron diffraction and given as

$\begin{equation} a=\alpha L \lambda, \end{equation}$

(2)

where $a$, $b$, $\alpha$, $i, j$, are presented in Figs. 11(a) and 11(b), respectively, $L$ is the camera length of the TEM, and $\lambda$ is the wavelength of the accelerated electron.

Usually more than three diffraction spots can be obtained from a single SAED pattern (Fig. 11(b)), hence Equation (2) becomes overdetermined. Therefore, to use all diffraction spots adequately and to reduce the uncertainty of the calculated results, the least-squares method is used in the data processing. In one word, the lattice parameters of a silicon nanobeam can be calculated from the SAED pattern of (100) silicon using Eq.(2). The results are presented in Fig. 12. The voltage of the comb drive actuator is used for representing different levels of tensile force. By statistically calculating the lattice parameters from more than 10 patterns of each driving voltage and using the least-squares fitting method to adequately use all diffraction spots in each pattern, it was possible to reduce the statistical measurement error to approximately 0.003 nm. Figures 12(a)-12(c) show that the lattice parameters $a$ and $b$ basically maintain a constant value, 0.553 nm. This result can be explained by the [110]-oriented stretched lattice model (Fig. 12(d)). As shown in Fig. 12(d), under the condition of small strain, under [110]-oriented tensile stress the [110] interplanar spacing would increase, while the [110] interplanar distance, perpendicular to the tensile stress, would decrease owing to the least-energy principle. The principle, in which the atomic bond that links two silicon atoms tends to remain constant, leads to the lattice parameters $a$ and $b$ being unchanged under a small stress and is also the fundamental mechanism of Poisson's ratio of a material. These results suggest that the trends of lattice parameters are in agreement with the increasing tensile stress model of the SCS nanobeam. Furthermore, the fact that the local strain calculated from the $\langle$110$\rangle$ stretched lattice model is consistent with the average strain of the nanobeam confirms the stress distribution uniformity of the SCS nanobeam.

4.3 Mechanical property and electrical property of Cu nanowire

The stress-strain relationship of Cu nanowire (220 nm in diameter) is presented in Fig. 13(a), which can be divided into two phases, elastic and plastic, as a typical metallic mechanical behavior. In the elastic phase, Young's modulus is determined to be 102.7$\pm$10.2 GPa, which is about 10-20 GPa lower than that of single-crystalline bulk copper ^[18], but still higher than the theoretical Young's modulus of 70-80 GPa for much smaller Cu nanowire (8 nm in diameter) predicated by MD simulation ^[24]. The maximum elastic strain turns out to be 1.3%. As the tensile stress reaches $\sim$1.37 GPa, the Cu nanowire begins to deform plastically and breaks at the strain of 6% when the stress reaches 2.2 GPa.

The $I$-$V$ curves of Cu nanowire under different tensile stress are demonstrated in Fig. 13(b), which exhibit nonlinearity and a symmetric characteristic with respect to zero bias. The simplest possibility for observing such nonlinearity of $I$-$V$ curves is generating a tunneling barrier at the wire-lead junction of the increasing voltage ^[25], which means the nonlinear curves may be caused by the existence of impurities (such as oxide) near the wire-lead contact junction. This theory is supported by the amorphous copper oxide coating the nanowire shown in Fig. 13(d). To explore the characteristic of the $I$-$V$ more precisely, the current was fitted as a function of the bias voltage into a Mclaurin series to the third power, which can be written as

$\begin{equation} I(U)=C_0+C_1U+C_2U^2+C_3U^3, \end{equation}$

(3)

where $I$ and $U$ are the current and voltage of the nanowire, respectively. From Eq. (3), the differential conductance at zero voltage is given as $\frac{{\rm d}I}{{\rm d}U}|_{U=0}=C_1$, which has the physical meaning of the original conductance of the Cu nanowire without any effect of voltage. Therefore, the reciprocal of coefficient $C_1$ is taken as the original resistance of nanowire at zero bias voltage. The fitted resistance under different tensile stress is shown in Fig. 13(c), which shows no obvious variation of resistance even when the nanowire exhibits plastic deformation. This result suggests that the dimensional variation of Cu nanowire during the tensile test has no significant impact on measured resistance. Furthermore, the resistivity of Cu nanowire is calculated to be 3.42 $\times$ 10$^{-2}$ $\Omega \cdot$cm, which is much higher than that of bulk copper (1.72 $\times$ 10$^{-6}$ $\Omega \cdot$cm reported in Ref. [26]) and pure Cu nanowire of a similar size (6 $\times$ 10$^{-6}$ $\Omega \cdot$cm reported in Ref. [27]). This can be attributed to the surrounding CuO, which has a much higher resistivity of electrical measurement that is estimated to be 10-20 k$\Omega$ by a four point measurement.

4.4 Mechanical property and electrical property of SiC nanowire

Stretching the SiC nanowire (320 nm in diameter) synthesized by normal pressure chemical vapor deposition, the stress-strain relationship of SiC nanowire is demonstrated in Fig. 14(a). Unlike Cu nanowire, the mechanical behavior of SiC nanowire reveals linearity until its fracture, which is a typical property of covalent material. Young's modulus of SiC nanowire is determined to be 203.5$\pm$20.7 GPa (Fig. 14(a)), which is lower than of its bulk form and most other reported SiC nanowires ^{[28, 29]}. On the other hand, a large scatter of measured values for Young's modulus is also reported in Ref.[28], which may be attributed to various allotropic states or the crystal quality of SiC, or the loading methods with respect to the crystalline planes. The high density of stacking defects on the (111) crystalline plane along the nanowire is shown in Fig. 14(d), which would cause the low Young's modulus. Nevertheless, the measured Young's modulus in our experiment is still compatible with the low limit reported in the literature. Also, the fracture strength turns out to be 7.5 GPa, which fits in the values range reported in Refs. [28, 30].

The $I$-$V$ curves of SiC nanowire under different tensile stresses are demonstrated in Fig. 14(b), where the linear property and piezoresistivity are revealed. The linear $I$-$V$ curves suggest that the nanowire and the testing device have a perfect ohmic contact. The resistivity of SiC nanowire is estimated to be 0.42-0.48 $\Omega \cdot$cm. This relatively low resistivity could explain the ohmic contact behavior. The measured resistance of the nanowire is about 285-320 k$\Omega$; on the other hand, the contact resistance of this experiment is estimated to be about 20k$\Omega$ by an additional four probe experiment, which means the estimated contact resistance is only 6%-7% of the measured resistance.

Furthermore, by eliminating the approximate contact resistance, the true resistance of SiC nanowire extracted from different tensile stresses is demonstrated in Fig. 14(c), which reveals the linear piezoresistivity as bulk SiC material does ^[31]. The increasing trend of resistance shown in Fig. 14(c) suggests that the nanowire is p-type doped, which has a positive gauge factor. The gauge factor of a piezoresistive material is given as ^[32]

$\begin{equation} {\rm GF}=\frac{\delta R}{\varepsilon R_{\rm n}}, \end{equation}$

(4)

where $\delta R$ is the incremental change in resistance, $\varepsilon$ is the strain of the nanowire, and $R_{0}$ is the resistance under zero stress. As a result, the gauge factor of the SiC nanowire is determined to be 14.1, which is of the same order of the value of p-type SiC fiber of 14 $\mu$m diameter reported in the literature (GF $=$ 5 reported in Ref. [29]) but slightly higher. The difference may be from different factors such as the resistivity, crystalline structure, fabrication process and so forth. For reference, the typical piezoresistive gauge factor of n-type bulk SiC is about $-13.2$ to $-41$^[33]. The fact that the gauge factor measured by our experiment fits in the range of p-type and n-type bulk SiC suggest that there is no obvious evidence of a nano-sized effect for piezoresistivity, which makes sense due to the comparably large diameter of our SiC nanowire (320 nm).

5. Summary

Utilizing our smart designed tensile testing device, mechanical and electrical characterization at the nanoscale can be represented and measured, which is important for the reliable design of micro/nanoscale devices. With three successful tensile tests for different nanomaterials, we have proved that a well designed tensile device based on MEMS technology can meet the requirements of the loading and measuring force, and the displacement with nanoscale resolution, which are big challenges in traditional methods. It can mean a MEMS tensile testing chip for in situ observation in SEM and TEM is controllable and reliable for fundamental investigations in nanoscale materials science, which has significant meaning for the designation and fabrication of nanodevices and also may accelerate its application in the future.