Tensile Testing of Microstructures
Method to Study the Mechanical Properties of Microsamples
- Fig. 1: Tensile test set-up and measurement process. (A) Image of the tensile testing set-up inside of a dual beam SEM/FIB chamber. An AFM cantilever attached to a support (here a simple screw nut) is used as a force sensor. The micromanipulator probe can operate the tiny object (here a silver wire) such as picking up, moving, and pulling. (B) Schematic of the test method and steps: picking up a wire (C1); fixing the wire on the AFM cantilever by Pt ion-induced deposition (C2); loading the wire by moving away the probe (C3); breaking the wire (C4).
- Fig. 2: Silver wire tensile testing. (A) FIB image of the wire before loading. The wire is fixed by ion-induced-deposition of Pt between the probe and the AFM cantilever edge. (B) The wire during loading. (C) The broken wire after the tensile test. Each tensile testing experiment is recorded on movie from side-view. All FIB images are taken from 52° to the object plane (0° stage angle). Scale bars are 10 µm.
- Fig. 3: Wire deviation before and after tensile test. (A) and (B) Top-view SEM images of the wire before and after test, illustrating that there is no significant deviation for the wire on the horizontal plane. (C) and (D) Side-view FIB images of the wire before and after the test. The end of the wire on the manipulator side is lower than that at the cantilever, suggesting that the wire shifts on the vertical plane (object plane). In order to monitor the deviation of the wire during the test, each experiment is recorded on movie from side-view. Scale bars are 10 µm.
- Fig. 4: Pulling the wires attached to one edge of the AFM cantilevers. (A) and (B) Top-view of a wire attached to the cantilever edge before and after loading. A rotation of the cantilever cannot be observed. (C) and (D) Repetition of the experiment with a a soft cantilever. Even if a large deflection takes place, no rotational deformation of the cantilever can be observed. Therefore, the wires can be fixed on the edge of the cantilever, which does not distort the experimental results but lowers the difficulty of manipulation. Scale bars are 10 µm.
- Fig. 5: The principle of the tensile testing experiment and a resulting stress-strain curve. (A) Scheme of the experimental principle. As the manipulator moves away, the cantilever is bent by a distance d, while the silver wire is stretched from its initial length L0 to L0+dL. The force Fh can be calculated as kd, where k is the force constant of the cantilever. Because the wire is tilted during loading, the actual force exerted on it is F=Fh/cos(θ), where θ is tilt angle of the wire. (B) Scheme of determining the true strain of the wire. Since the angle between ion-beam and the object plane a (light blue plane) of cantilever and wire is 52°, the recorded length (black line) of the wires is the projection of the true wire length (blue line) on the image plane b. the angle between plane a and b is 38°. Therefore, one can calculate the true length of the wire and then obtain the strain of the wire. (C) Plot of a stress versus strain curve of a wire with a diameter of about 560 nm.
The small size of micro- and nano-structures makes tensile testing challenging. In this study we meet this challenge by combined use of a Focussed Ion Beam (FIB) in Dual Beam configuration, an AFM-cantilever, and a micromanipulator which provide the required accuracy and versatility to measure the mechanical properties of nanowires by tensile testing. AFM cantilevers with a big range of force constants principally enable us to measure the tensile behavior of a great variety of materials.
The accelerating pace of technological miniaturization e.g. development of micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS) has attracted much attention of researchers during the last decade. Due to the superior mechanical properties of micro- and nano-structures such as nanowires and nanotubes , these have been proposed as new building blocks for novel device architectures. In order to improve and optimize their application and fully utilize their special material properties we need to understand the governing deformation mechanisms. Uniaxial tensile tests are the most commonly performed deformation experiments, which provide basic information on the mechanical properties. Tensile testing is generally preferred, because the stress and strain state in the sample is nominally uniform and the interpretation of data is relatively simple compared to compression experiments. Yet, the hurdle for executing tensile tests at the micro- and nanoscale is high as accurate and reliable testing is limited by experimental uncertainties. Herein, we report a method to characterize mechanical properties of micro- and nanoscale objects by tensile testing, solving the main challenges encountered for micro objects. Our method is based on using an AFM cantilever and a micromanipulator with assistance of FIB/SEM. Preparation and FIB/SEM microscopy is quite simple but can extract precise quantitative data. This method not only provides high accuracy but also offers high versatility by using customized load ranges of different AFM cantilevers.
Experimental Challenges of Microtensile Testing
The main challenges, according to reviews  , are as follows:
Sample harvesting, manipulation, and gripping
A micromanipulator with the assistance of FIB/SEM can locate, attach, transfer, and manipulate micro objects to the desired testing platform. The manipulation process can be achieved with moderate handling damage mainly due to ion beam cutting or ion-induced metal deposition. Our method uses commercially available Dual-Beam-FIB (FEI STRATA 400 Stem) and micromanipulator systems (Omniprobe). The sample gripping for tensile tests can be accomplished by using local electron- or ion-beam induced Pt deposition. The deposited Pt pads are robust enough to hold during testing.
Small-scale tensile tests require the measurement of tiny forces due to the small sample size. AFM cantilevers are used as load sensors in our method, where in principle the optical system of the AFM is replaced by the FIB/SEM. In the AFM the cantilever is sensitive to very small forces, even forces between atoms can be determined due to the optical detection system used there. The measurement is based on cantilever bending  under pressure  or lateral load , so interpretation of the obtained data is challenging in contrast to data obtained from uniaxial mechanical tests. Ruoff et al. was the first, who performed tensile tests on carbon nanotubes using AFM cantilevers . Orso et al. combined the AFM and FIB techniques to measure the tensile strength of biological samples using piezoresistive AFM cantilevers , which are expensive and are not as sensitive as normal ones. With our first prototype we measured the yield strength of copper wires without determination of a stress-strain curve . Here we use a normal AFM cantilever as load sensitive sensor to measure the tiny forces leading to deflections of the cantilever. Furthermore, an AFM cantilever based load measurement system offers a high versatility since the load range can be customized to suit the testing need simply by changing the AFM cantilever.
In the case of in-situ tensile tests, differential digital image tracking (DDIT) is an ideal method for strain measurement with SEM or FIB used as image sources during testing . This method can achieve a resolution of up to a thousandth of a pixel. You can find details of the DDIT method in Gianola & Eberl and references therein . The DDIT method has been adapted to our needs in order to measure the strain with the FIB as image source.
Figure 1 shows an image of the experimental setup inside of a dual beam SEM/FIB chamber and the steps of the tensile testing procedure. An AFM cantilever used as a force sensor is selected depending on the sample's properties and attached to a support (here a simple screw nut). Single crystalline silver wires with their longitudinal axis in the  direction are used as test specimens. They have been transferred to a silicon substrate and placed in the FIB chamber (fig. 1A and C1). The micromanipulator is used to harvest and align the specimen (C1), then after cutting to the appropriate length to transfer it to the AFM cantilever (B). The manipulator moves and touches a silver wire, which is welded on the tip of the manipulator by ion-induced-deposition of Pt. By driving up the probe, an individual wire is lifted up from the silicon substrate (fig. 1C1), then transferred to the tip of the cantilever, and finally fixed to it by Pt deposition (fig. 1C2). The wire also can be welded on the side edge of the cantilever, which is easier to handle. In our experiment a force is applied by driving the manipulator to the right, away from the cantilever with a constant speed of 0.1 µm/s, leading to a deflection of the cantilever (fig. 1C3). The deflection can be used to calculate the force exerted on the wire. The probe continues moving until the failure of the wire takes place (fig. 1C4). The whole tensile loading experiment is recorded on movie from side-view using FIB as image source. By analyzing the digital movie, the force and strain information can be obtained for every image by measurement of the deflection of the cantilever and can be calculated by measuring the stretched wire length and its initial length. Finally, the stress-strain curve can be plotted.
Figure 2 shows the actual tensile testing of a silver wire fixed between the AFM cantilever and the manipulator (fig. 2A). Ion-beam induced deposition of Pt pads was used for fixing, which has been proved as an efficient way to attach the specimen. The images of each test were taken as movie from the side-view with FIB at a stage angle of 0° corresponding to an angle of 38° between object plane and imaging plane. The angle between electron column and ion column in our Dual Beam FIB is 52°. Fig. 2B shows the setup during loading. When the manipulator moves to the right to pull the wire, the AFM cantilever is bent due to the force applied on the wire. When the load is too high the wire breaks as shown in fig. 2C. It is worth to point out that the probe moves down in comparison to the initial position (see fig.5A).
As shown in the fig. 2C, after the tensile test, one end of the silver wire is localized at a lower position compared to the other end. To avoid an additional contribution from bending forces of the wire, it is essential for the experiment to the keep the deviation from the ideal line (wire being in object plane and perpendicular to the cantilever ) low, which can be achieved by careful pulling and simultaneously applied positional corrections with the manipulator. The deviation can be separated into the horizontal plane and vertical plane respectively. Fig. 3 shows, that there is almost no deviation, that is no shift on the horizontal plane from top-view, revealed by SEM images (A, B), while significant deviation in the vertical plane can be observed from side-view FIB images (C, D), before and after the test. In order to monitor the deviation on the vertical plane and exactly determine the applied forces, the movies of the experiments have to be recorded from side-view by FIB imaging. Although the ion beam can possibly damage the specimens , the lowest ion beam current (1.5pA) and shortest dwell time (50ns) were used to reduce the overall beam damage, corresponding to an ion irradiation dose of about 9.4 x 106 ions/s or 4.24 x 105 ions/frame (here 1024 x 884 pixel with 45 ms/frame). Short exposure times (< 1min ) reduce the damage of the ion beam irradiation to a minimum, no significant surface damage could be observed after the measurement.
Attaching the wire to the side-edge of the AFM cantilever is experimentally easier than on the tip. However, this is only possible if there is no significant torsion on the AFM cantilever. This was tested by the experiment shown in fig. 4. The silver wire is attached on the edge of the cantilever. The SEM images are taken before and after loading from top-view (fig. 4 A and B). No noticeable rotation of the cantilever can be observed, suggesting the torsion effect is negligible. In order to further prove this point, we repeated the experiment by replacing the cantilever with a very soft one. As in the previous experiment, this cantilever also showed no rotation despite of much stronger deflection at the soft cantilever. Therefore, the edge attachment configuration is adapted during our experiments.
Stress and Strain Calculation
Accurate tensile testing requires accurate force and strain measurement. Force measurements can be done by measuring the deflection distance of the cantilever during testing. The force, Fh, can be calculated as kd, where k is the force constant of the cantilever - here 46N/m. Because the wire is tilted during loading (fig. 3B), the actual force exerted on it is F=Fh/cos(θ), where θ is the tilt angle of the wire. The other important point is the measurement of the strain. In the case of in-situ tensile testing, DDIT is an ideal method for strain measurement based on the FIB images obtained during testing. For this procedure, a series of FIB images is captured from a movie recorded during testing. The grey values of a linear profile along the wire are extracted using ImageJ software . The displacement of the differential increase of the grey values, generally appearing as two well defined separate peaks, which resemble both ends of the wire, is converted into strains that can be determined with high resolution, even sub-pixel resolution is achievable using certain evaluation algorithms . More peaks arising from particular image features can be selected to improve the accuracy. Since the angle between FIB beam and horizontal plane is fixed at 52°, the recorded length (black line) of the wires is a projection of the true length of the wire (blue line) on plane b (fig. 5B). Therefore, we can calculate the true strain by measuring the projected elongation difference between initial and stressed wire. Finally, the stress-strain curve can be plotted as shown in fig. 5C. The curve shows mainly an elastic curve progression until failure of the wire.
We have developed a simple method to characterize mechanical properties of micro- and nano-scale objects by tensile testing based on commercially available FIB and micromanipulator systems. The micromanipulator can be used with the FIB system to locate, harvest, manipulate, and mount small specimens with minimal handling damage. The whole set-up is very simple but gives good quantitative results. The loading force is extracted from the deflection of AFM cantilevers with high precision. Strain is measured by the DDIT method using FIB images, which can achieve a very high precision with the help of image processing software including refinement algorithms. This method provides high accuracy and also offers a high versatility due to commercially available AFM cantilevers with a great variety of force constants, allowing to test materials in a wide strength range.
The authors would like to thank Tobias Heiler for help creating the 3D graphics.
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Dr. Torsten Scherer (corresponding author)
Dr. Sheng Zhong
Prof. Dr. Thomas Schimmel
Institute of Nanotechnology
Karlsruhe Institute of Technology
Dr. Sheng Zhong,
Prof. Dr.Thomas Schimmel
Institute of Applied Physics and Center for Functional Nanostructures (CFN)
Karlsruhe Institute of Technology