A Multi-step Method for In Situ Mechanical Characterization of 1-D Nanostructures Using a Novel Micromechanical Device
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- Lu, Y., Ganesan, Y. & Lou, J. Exp Mech (2010) 50: 47. doi:10.1007/s11340-009-9222-0
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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.
KeywordsMicromechanical deviceIn situ NanoindenterFEA1D nanostructure
Finite element analysis
Scanning electron microscope
Transmission electron microscope
Atomic force microscope
Silicon on insulator
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 [1–4], 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  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.  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 . On the other hand, Zhu et al.  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.  developed a fatigue testing platform that consisted of an electrostatically actuated comb drive actuator and a capacitive displacement sensor. Kahn et al.  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.
Micromechanical Device Development and Modeling
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 .
Multi-step Methodology Development
Step 1: FEA Model Calibration
Step 2: Determination of Actual Sample Young’s Modulus
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.
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 [1–4].
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  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.
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.