Experimental Mechanics

, Volume 50, Issue 1, pp 47–54

A Multi-step Method for In Situ Mechanical Characterization of 1-D Nanostructures Using a Novel Micromechanical Device

Authors

  • Y. Lu
    • Department of Mechanical Engineering and Materials ScienceRice University
  • Y. Ganesan
    • Department of Mechanical Engineering and Materials ScienceRice University
    • Department of Mechanical Engineering and Materials ScienceRice University
Article

DOI: 10.1007/s11340-009-9222-0

Cite this article as:
Lu, Y., Ganesan, Y. & Lou, J. Exp Mech (2010) 50: 47. doi:10.1007/s11340-009-9222-0
  • 404 Views

Abstract

A novel micromechanical device was developed to convert the compressive force applied by a nanoindenter into pure tensile loading at the sample stages inside a scanning electron microscope or a transmission electron microscope, in order to mechanically deform a one-dimensional nanostructure, such as a nanotube or a nanowire. Force vs. displacement curves for samples with Young’s modulus above a threshold value can be obtained independently from readings of a quantitative high resolution nanoindenter with considerable accuracy, using a simple conversion relationship. However, in-depth finite element analysis revealed the existence of limitations for the device when testing samples with relatively low Young’s modulus, where forces applied on samples derived from nanoindenter readings using a predetermined force conversion factor will no longer be accurate. In this paper, we will demonstrate a multi-step method which can alleviate this problem and make the device capable of testing a wide range of samples with considerable accuracy.

Keywords

Micromechanical deviceIn situ NanoindenterFEA1D nanostructure

Abbreviations

MEMS

Micro-electro-mechanical systems

FEA

Finite element analysis

SEM

Scanning electron microscope

TEM

Transmission electron microscope

AFM

Atomic force microscope

1-D

One-dimensional

SOI

Silicon on insulator

Introduction

One-dimensional nanostructures, such as metallic nanowires and carbon nanotubes, have stimulated great interest recently as important building blocks for nanoscale electronic and electromechanical devices used in various applications. However, the ability to achieve the full potential of these fascinating technologies is ultimately limited by how these one-dimensional nanomaterials will behave at relevant length scales. Although significant progresses have been made on mechanical testing of 1-D nanostructures using existing techniques such as AFM based bending methods [14], performing direct uni-axial nanomechanical characterization of an individual nanowire or nanotube, still remains a challenge.

Numerous MEMS devices developed to perform mechanical testing on 1-D and 2-D nanostructures have recently emerged due to the following reasons: (1) Knowledge of MEMS technology accumulated in the past decades have enabled the development of a wide range of device designs for different testing purposes and configurations, with excellent statistical representations; (2) The compact size of a MEMS device makes it ideal to test samples with nanometer dimensions. This property also makes them suitable for in situ testing within various microscope vacuum chambers; (3) The quantitative nature and high displacement/force resolution obtainable through MEMS device based measurements makes them especially attractive for nanomechanical testing. Due to the large amount of literature available in this area, only a brief review of some representative devices specifically designed for nanomechanical testing of samples with nanometer dimensions will be given.

There are two broad categories of design concepts for MEMS based nanomechanical testing platforms in terms of actuation and sensing mechanisms: one relies on external equipment for loading or sensing, and the other has built-in on-chip actuators and/or sensors. The MEMS-based in-situ TEM tensile testing bed developed by Haque and Saif [5] to characterize free-standing nanoscale thin films is an example of a device that falls under the first category. Also falling under the same category are the polysilicon MEMS structures fabricated by Boyce et al. [6] in order to study strength distributions in freestanding polysilicon layers. Another example of this type of devices is a MEMS test bed using external AFM piezoelectric actuation and optical digital image correlation method for displacements measurements [7]. On the other hand, Zhu et al. [8] designed an on-chip nanoscale tensile testing platform for testing 1D nanostructures and thin films that consisted of a thermal/electrostatic actuator for load application and a differential capacitance load sensor for displacement and load measurement. Muhlstein et al. [9] developed a fatigue testing platform that consisted of an electrostatically actuated comb drive actuator and a capacitive displacement sensor. Kahn et al. [10] designed a comb-drive based MEMS device to test nanoscale biological materials, in which electrostatic actuation was again used to drive the shuttles across which the samples were clamped, while simple cantilever beams were used to monitor the force applied on the specimen. All three of the latter are examples of devices that fall under the second category. Devices falling under either of these two categories of MEMS-based nanomechanical testing platforms have their own set of advantages and disadvantages and they both offer numerous possibilities to test nanoscale samples with considerable accuracy.

Recently we designed and fabricated a micromechanical device, which in conjunction with a quantitative nanoindenter can perform uni-axial tensile testing on 1-D nanoscale samples [11], using established micro-fabrication processes. Using this device, compressive force applied by a quantitative in situ SEM/TEM nanoindenter can be converted into pure tension loading at the sample stages in order to mechanically deform a one-dimensional nanoscale sample, such as a nanotube or a nanowire. At the same time, the underlying deformation process could be monitored by high resolution electron microscopy. It is noted that similar push-to-pull idea was explored in the past such as the Theta sample development [12, 13] and a method to measure intrinsic strain in thin films [14]. Our preliminary finite element analysis (FEA) showed that the force vs. displacement curves for the tested samples can be obtained independently from the readings of the nanoindenter using simple conversion factors. For example, for a 5 μm long Ni nanowire sample having a 300 nm diameter, the force conversion factor, defined here as the ratio of the force acting on the sample to the force applied by the indenter on the top shuttle in the negative y direction (see Fig. 1), was found to be 0.666 and the displacement conversion factor, defined here as the ratio of the nanoindenter tip displacement to the sample stage displacement (in the presence of a sample i.e. the nanowire, sample stage displacement can be interpreted as the elongation of the sample) [11], was found to be ∼0.987. Both these values were obtained via FEA modeling (the Young’s modulus of the Ni nanowires was assumed to be the same as that of bulk Ni i.e. 200 GPa). Both these conversion factors remain valid, though not extremely accurate, for metal nanowires having dimensions similar to the one described above and having a Young’s modulus value greater than ∼100 GPa. However, our in-depth FEA indicated that this simple relationship will no longer hold when testing samples have relatively low Young’s modulus. Under these conditions, forces vs. displacement curves derived from the nanoindenter readings using the aforementioned conversion factors will no longer be accurate. In order to address this issue, we present a multi-step method which would enable the use of this device for the characterization of a wide range of samples with considerable accuracy. Briefly, the first step involves making suitable corrections to the parameters of the FEA model of a device, such that its behavior closely resembles that of the actual device (without a mounted sample). This step is to make sure our FEA model is properly calibrated against the real device performance and is ready for subsequent analyses. Next, a series of virtual experiments must be conducted using a device loaded with virtual samples with varying Young’s moduli. The FEA simulated system stiffness Ks obtained (Ks = (force applied by indenter tip)/(displacement of top shuttle when sample is loaded in device)) must then be plotted as a function of sample Young’s modulus. The Young’s modulus for a real sample with unknown material properties can thus be determined from above plot, using the Ks value derived from the linear portion of force–displacement curve of an actual nanoindenter driven experiment. The second step is taken because the FEA simulated stiffness of the sample loaded device will depend on sample modulus and this relationship needs to be explicitly established in order to accurately test a material with unknown material properties using the FEA derived force and displacement conversion factors. In the third and final step, another FEA simulation must be performed using the previously determined “true” sample Young’s modulus in order to obtain the actual force and displacement conversion factors for this specific sample. We can then use these conversion factors to independently obtain the complete experimental force vs. displacement curve for the aforementioned sample. Additionally, in this paper, we also aim to discuss the range of sample Young’s modulus within which the device can be operated with acceptable accuracy using fixed conversion factors. It is worth noting that, compared to the force conversion factor which relies solely on FEA simulations, the displacement conversion factor is less problematic since the sample elongation could be detected and measured directly inside SEM or TEM from image analysis. It is for this reason that we chose to focus on the force conversion factor determination in this paper.
https://static-content.springer.com/image/art%3A10.1007%2Fs11340-009-9222-0/MediaObjects/11340_2009_9222_Fig1_HTML.gif
Fig. 1

Schematic of the micromechanical device

Micromechanical Device Development and Modeling

The devices described in this paper were developed to perform quantitative tensile experiments on 1-D nanostructures to avoid potential buckling instability of samples with high aspect ratio. It is a passive type of a MEMS device where application and measurement of load and displacement can be realized with the aid of a quantitative nanoindenter housed within the vacuum chamber of a SEM or a TEM. The force and displacement resolution of the nanoindenter lies in the order of a few tens of nano-Newtons and a few angstroms respectively. The geometry of the device is shown in Fig. 1. It basically consists of a pair of movable shuttles (as the sample stage) that are attached to a top shuttle via 60° inclined freestanding chevron beams. Devices investigated in this work were fabricated on <100> oriented p-doped silicon on insulator (SOI) substrates, with 9.5 μm thick device layer. The fabrication scheme adopted involved the use of dicing lines on the masks such that individual devices could be isolated from the wafers on 2 mm × 3 mm pieces, which could in turn be fitted onto a TEM sample holder. A window under the specimen area of the device was micro-fabricated to ensure electron beam transparency for in situ TEM experiments and to also facilitate nanoindenter head positioning (Fig. 2).
https://static-content.springer.com/image/art%3A10.1007%2Fs11340-009-9222-0/MediaObjects/11340_2009_9222_Fig2_HTML.gif
Fig. 2

SEM image showing the geometry of the fabricated device and the nanoindenter tip. Arrows show the direction of movement of the top shuttle and sample stage shuttles upon load application. The inset shows a close up image of a mounted Ni nanowire sample

The actuation mechanism for the devices involves the usage of a nanoindenter inside a SEM or a TEM to apply a load on the top shuttle of the device in the vertical (Y) direction. Four sets of symmetrical inclined beams transform the vertical motion of the top shuttle into a horizontal (X) translation of the sample stage shuttles. Proper alignment of the nanoindenter head would result in the sample stage shuttles moving symmetrically in the negative Y direction, thus ensuring that the sample, clamped across the sample stage shuttles, experiences axial tensile loading in X direction (Fig. 2). The system is purely mechanical as opposed to most of the existing techniques that involve electro-mechanical or thermo-mechanical coupling. The simple design helps minimize the sources of errors, and the use of a quantitative nanoindenter ensures reliable results with a sufficiently high resolution [11].

The device behavior under mechanical loading, both in the presence or the absence of a mounted virtual sample, was modeled using FEA (ANSYS™) in order to determine the relationship between the load applied by the nanoindenter and the force acting on the sample stage/sample, and the relationship between nanoindenter tip/top shuttle displacement and sample stage displacement/sample elongation. The modeling was done using the plane stress model employing a device layer thickness of 9.5 μm. The Plane 42 elements meshing were employed in our current study. More complex Plane 82 elements were also employed and it was found that there was no significant difference between these two elements for this device. The devices were assumed to be operating in the linear elastic regime and the material properties were assumed to be isotropic. For all analyses, the Young’s modulus and Poisson’s ratio of silicon were assumed to be 160 GPa (value obtained via independent nanoindentation experiments conducted on the actual device) and 0.278 [15] respectively. A 5 μm long virtual nanowire with a 300 nm diameter was used to model the device behavior in the presence of a mounted sample. Figure 3 shows the meshing of the device as well as a clamped virtual nanowire sample.
https://static-content.springer.com/image/art%3A10.1007%2Fs11340-009-9222-0/MediaObjects/11340_2009_9222_Fig3_HTML.gif
Fig. 3

Finite element meshing of the micromechanical device clamped with a 5-μm long nanowire between two sample stage shuttles (The inset shows a close up image of a mounted sample)

Multi-step Methodology Development

Step 1: FEA Model Calibration

In order to calibrate our finite element model constructed based on design parameters against the behavior of actual device, calibration experiments were done on devices with no sample mounted. This first step is necessary since the geometrical dimensions of the fabricated device generally differ from the original design due to the anomalies introduced by the fabrication process. By varying the thickness and other geometrical parameters(such as chevron beam width) using measurements obtained from actual device and then compare the simulated and experimental force–displacement curves, we calibrated the FEA model of device and make sure its behavior during virtual experiments closely resembles that of the actual device in the absence of a mounted sample, e.g. the device stiffness Kd (Kd = (force applied by indenter tip)/(displacement of top shuttle when no sample is loaded)) obtained in simulation closely follow Kd from the actual calibration experiment (Fig. 4).
https://static-content.springer.com/image/art%3A10.1007%2Fs11340-009-9222-0/MediaObjects/11340_2009_9222_Fig4_HTML.gif
Fig. 4

Measured and simulated micromechanical device calibration profile (blue triangles show the experimental data from one nanoindentation test on an empty device, and red squares show FEA data of the calibrated model)

Figure 5 shows the X and Y nodal displacement contour for a device, without a mounted sample on it, upon load application on the top shuttle. The X direction displacement contour shows that two shuttles move in opposite directions along X axis upon load application. With testing specimen loaded, this value can be naturally considered as the extension of the sample. The Y direction displacement contour was used to calculate the device stiffness Kd. For example, the stiffness Kd of one particular micromechanical device was determined to be ∼438 N/m by averaging the results of several independent indentation experiments on device without mounted sample on it. After making a few adjustments according to the actual measurement of the as-made devices, such as beam width and thickness, to the dimensions of the FEA model of the device, a similar value for Kd was obtained via simulation.
https://static-content.springer.com/image/art%3A10.1007%2Fs11340-009-9222-0/MediaObjects/11340_2009_9222_Fig5_HTML.gif
Fig. 5

(a) X axis nodal displacement contour of the micromechanical device and (b) Y axis nodal displacement contour of the micromechanical device, without a mounted sample, upon load application on the top shuttle (unit: μm)

Step 2: Determination of Actual Sample Young’s Modulus

Once the FEA model of empty device has been appropriately calibrated, we can focus our attention on samples with unknown material properties (here we focus on the Young’s modulus). A virtual 1-D sample having a geometry similar to the sample which is to be tested in real time (in our case we used a 5 μm long nanowire having a 300 nm diameter) was clamped onto the FEA model of the device (Fig. 3). A series of FEA simulations under different applied loading levels were performed while varying Young’s modulus of the mounted sample. By determining the Y direction nodal displacements of the device’s top shuttle at different applied loads, the system stiffness Ks, was obtained and plotted as a function of Young’s modulus of the virtual sample (Fig. 6).
https://static-content.springer.com/image/art%3A10.1007%2Fs11340-009-9222-0/MediaObjects/11340_2009_9222_Fig6_HTML.gif
Fig. 6

Young’s modulus of a virtual nanowire sample as a function of system stiffness Ks (the red arrow indicates a Ks value of 3,571 N/m obtained from a preliminary test for a device mounted with a 300 nm-diameter nickel nanowire)

Shown in Fig. 6 is a plot of system stiffness (Ks) vs. mounted sample’s Young’s modulus. In order to determine the Young’s modulus of the sample to be tested in real time, the Ks value of the device with the mounted sample must first be determined from the linear portion of the force–displacement curve of the nanoindenter driven experiment conducted in real time. This Ks value can in turn be used to ascertain the Young’s modulus for the sample using the plot shown in Fig. 6. For example, a Ks value of ∼3571 N/m was obtained for a device mounted with a 300 nm-diameter nickel nanowire in our preliminary experiments conducted in real time. Using the plot in Fig. 6 (as indicated by the red arrow), the Young’s modulus for this nanowire was ascertained to be 120 ± 12 GPa, a value that is lower than the Young’s modulus of bulk nickel (200 GPa). This value is consistent with an AFM force-deflection method determined Young’s modulus value (124 ± 8 GPa) of a 300 nm-diameter nickel nanowire that was fabricated from the same batch. Additional experiments are planned to further investigate this anomaly in elastic properties of nickel nanowires. It is important to realize that other factors such as indenter tip alignment and specimen attachment and alignment will also affect our measurement results which could contribute to the uncertainties of this method.

Step 3: Determination of Conversion Factor

In the third and final step, our goal is to obtain the “true” force conversion factor for the device mounted with the sample that is to be characterized. This is a critical step to realize the quantitative nature of the micromechanical devices in conjunction with the high resolution in situ SEM/TEM nanoindenter.

This step involves the usage of the fixed value of Young’s modulus obtained from step 2 in order to perform another FEA simulation following above steps. The procedure is similar to the one described in step 2, but we pay close attention on the X direction displacement under a prescribed top loading, since it provides the strain of the nanowire specimen. Therefore, the actual force loaded on the nanowire sample can be calculated based on its strain and dimensions, as well as Young’s modulus obtained above. Thus the actual force conversion ratio of the device system loaded with the specific sample will be obtained. For example, in the case of the same 300 nm diameter nickel nanowire, based on the Young’s modulus value determined in step 2, a force conversion factor of 0.65 was obtained via simulation using the modified FEA model. We believe that compared to the force conversion factor we previously reported, which was based on the Young’s modulus of bulk Ni, the value obtained via this novel method is more accurate. In addition, using the X and Y direction nodal displacements contour, the displacement conversion factor between the nanoindenter/top shuttle and the sample stages was also determined. Note this displacement conversion factor could also be determined via imaging of the SEM or TEM for experiments performed in situ.

Discussion

As mentioned earlier, when using the nanoindenter actuated micromechanical device for in-situ experiments, we rely solely on the load signal readings from the nanoindenter in order to determine the applied force on samples. Therefore, determination of force conversion factor is of critical importance as its accuracy greatly affects the computed applied force thus stress on the sample. It has been demonstrated that the newly developed multi-step method can enable us to obtain more accurate force conversion factor than the one based on bulk material Young’s Modulus values. This clearly demonstrates the importance of this method especially when testing samples with nanometer dimensions, due to the possible size effects in mechanical properties of materials at small length scales [14].

When using the micromechanical devices as a mechanical testing platform for 1D nanomaterials, it is always advantageous to have fixed force and displacement conversion factors with a tolerable error margin. Hence, it is important to find an appropriate sample elastic property range within which simple fixed conversion factors could still be reliably used with reasonable accuracy. For this purpose, we conducted a series of finite element simulations to study the variation of force conversion factors with different sample Young’s modulus. Again we apply a prescribed loading on device clamped with a virtual nanowire sample and vary the Young’s modulus of the sample, as in step 2. Then we calculated the forces resulted on sample through the X displacements (extensions) of the nanowire samples, similar to the step 3. So the force conversion factor will be obtained as a function of sample Young’s modulus (Fig. 7) under specific loading. From looking at the plot shown in Fig. 7, the following observations can be made: (1) force conversion factor increase with increase in the sample Young’s modulus; (2) at values close to 500 GPa and above, the force conversion factors gradually approach an asymptotic value of ∼0.7 for a wide range of sample Young’s modulus; (3) for samples with relatively small values of Young’s modulus (i.e. below ∼100 GPa), the force conversion factor increases dramatically with increase in sample Young’s modulus. It might be reasonable to say that for samples having a Young’s modulus value greater than ∼100 GPa, the force conversion factor could be approximated to 0.666 with relatively good accuracy (less than 5% error). On the other hand, using a curve similar to the one shown in Fig. 7, force conversion factors can be computed with much greater accuracy. Another important implication of this study is that since the device stiffness can be tailored through the number and dimension of the connecting chevron beams, it is possible to design a device such that the force conversion factor becomes a constant even for small values of sample Young’s modulus, and make the device capable of testing such materials with high accuracy. It is also worth mentioning that the factor of machine compliance has been taken into consideration of our nanoindenter setup inside SEM/TEM chamber and calibration experiments were done to get the correct machine compliance value before the actual measurements.
https://static-content.springer.com/image/art%3A10.1007%2Fs11340-009-9222-0/MediaObjects/11340_2009_9222_Fig7_HTML.gif
Fig. 7

Force conversion factor (ratio between force experienced by sample and force applied by nanoindenter) as a function of sample Young’s modulus

Conclusions

The effect of sample Young’s modulus on the force conversion factor of a nanoindenter actuated micromechanical testing platform has been examined extensively using finite element analysis. Our simulation demonstrated that the force applied on a 1-D nanoscale sample mounted on the micromechanical device using a quantitative nanoindenter varies quite dramatically with variation in sample Young’s modulus, especially for samples have a value of Young’s modulus lower than 120 GPa. A multi-step method to overcome this limitation has been proposed. This method involves the usage of both FEA simulations and actual indentation experiments. Force conversion factors computed using this technique are considered to be more accurate than the ones reported earlier [11] since the latter were derived from simulations that were based on the bulk Young’s modulus of the sample material. The technique provides a viable solution for obtaining accurate force–displacement or stress–strain curves for 1D nanoscale samples with unknown properties. We emphasize that this multi-step method is particularly useful for nanoscale samples due to the well-known size effects in mechanical properties of materials. Finally, it is worth noting that the geometrical design of our MEMS based micromechanical device can be modified for testing a wide range of nanomaterials with high accuracy.

Acknowledgments

This work was supported by National Science foundation grant NSF ECCS 0702766 and by Air Force Research laboratory grant AFRL FA8650-07-2-5061. The authors gratefully acknowledge Brian Peters (MTS Nano Instruments, Oak Ridge, TN), Ryan Stromberg and Richard Nay (Hysitron Inc., Minneapolis, MN) for the help they provided with device testing. The authors would also like to thank Dr. J. E. Akin and Xiaoge Gan (Rice University, Houston, TX), Dr. A. Minor (Lawrence Berkeley Lab, Berkeley, CA), Dr. R. Ballarini (University of Minnesota, Minneapolis, MN) for useful discussions.

Copyright information

© Society for Experimental Mechanics 2009