**7. Strain measurement**

The measurement of strain is the most challenging part of the tensile testing of thin film specimens. Due to the small size of thin films, none of the current macro-scale methods of strain measurement are applicable to tensile testing of thin films. Thin film specimens are at the same size scale of resistive strain gages and are too small for LVDT-based extensometers. Technically, any method of strain measurement that is used in contact with the specimen is not useful. Therefore, many researchers have developed or adapted non-contact strain measurement techniques to measure the strain during tensile testing. These techniques can be categorized into four different groups, including cross-head displacement; optical imaging; interferometry-based methods; and advanced microscopy techniques like AFM, SEM, and TEM for *in situ* strain measurement. In what follows, these methods are discussed in detail.

Having prepared the samples and mounted them in grippers, they had to be loaded to the required load level and the load value has to be measured. With the availability of different types of commercial actuators and load cells, this part of a tensile testing setup is not as challenging as the other parts. Piezo driven actuators were among the popular tools for loading. These actuators provide the capability of loading the specimen with different waveforms and frequencies. If they are fitted with any type of displacement sensor, e.g. strain gage, LVDT, or capacitive sensors, they can be controlled in a close-loop system in order to compensate for hysteresis and drift. On the other hand, this displacement feedback can be recorded as the cross-head displacement and be used for the measurement of strain. Many of the research works discussed earlier in this chapter are equipped with this type of actuators (Read & Dally, 1993; Cornella, 1999; Sharpe et al., 1997; Zupan & Hemker, 2001; Allameh et al., 2004). Inchworm (Chasiotis & Knauss, 2002) and motor-driven micrometer (Ruud et al., 1993) actuators are also among the type of actuators that were used for specimen loading. Sharpe & Bagdahn, 2004 used a loud-speaker operating at 20 kHz in their early fatigue tests on polysilicon to dynamically load their specimens at high frequencies. Almost all research groups used strain gage-based load cells to measure the applied load and hence the stress. Tajik, 2008 also used piezoelectric actuators along with precision strain gage load cells that can provide static and dynamic loading capabilities to test thin film

A specific group of tensile test setups are those that have integrated the load-actuation and measurement with the specimen itself on a MEMS-based tensile testing device. These devices provide much higher resolution for load actuation and load measurement, making them a versatile tool to study the mechanical properties of nano-scale structures like carbon nanotubes and nano-wires (Zhu et al., 2007), and films that are substantially thin or have very small gage section areas. (Haque & Saif, 2004) On the other hand, because of their small size, they can be used for *in situ* study of deformation in Scanning Electron Microscope (SEM) or Transmission Electron Microscope (TEM). (Zhu et al., 2003; Haque & Saif, 2003, 2004; Samuel & Haque, 2006; Rajagopalan et al., 2007) However, these devices are not so applicable at the length scale where most of the thin films are usually fabricated and used in

The measurement of strain is the most challenging part of the tensile testing of thin film specimens. Due to the small size of thin films, none of the current macro-scale methods of strain measurement are applicable to tensile testing of thin films. Thin film specimens are at the same size scale of resistive strain gages and are too small for LVDT-based extensometers. Technically, any method of strain measurement that is used in contact with the specimen is not useful. Therefore, many researchers have developed or adapted non-contact strain measurement techniques to measure the strain during tensile testing. These techniques can be categorized into four different groups, including cross-head displacement; optical imaging; interferometry-based methods; and advanced microscopy techniques like AFM, SEM, and TEM for *in situ* strain measurement. In what follows, these methods are discussed

**6. Load actuation and measurement** 

specimens as thin as 300 nm.

MEMS and microelectronics applications.

**7. Strain measurement** 

in detail.

Read & Dally, 1993 monitored the cross-head displacement and used it as a measure for strain. There are many sources of error involved in this technique. Specimen may slip at the gripper. On the other hand, the gripper itself may have clearances that cause backlash during the changes in load direction. Compliance of the test setup is the other source that deteriorates the accuracy of the method. The cross-head displacement is a combination of all of the deformations in the load train, i.e. the deformations in load-cell, load actuator, the test rig, grippers and albeit in the specimen itself. Therefore, this measurement will not provide an accurate measure of stain in the gage section of the sample.

Cornella, 1999 measured the compliance of the test setup by compressing the load actuator to the load cell in the absence of specimen and subtracted this compliance from the actual measurements to find the deformation in the specimen. They reported that 76% of the measured displacement accounts for the actual deformation in the specimen (Zhang et al., 2006). In order to validate the strain relaxation measurements and to show that the drop in the stress level over time is the actual behavior of the specimen itself and not the test setup, they used iridium specimens. Iridium, due to its high melting point, has a very low relaxation at room temperature. Since these tests revealed no relaxation, they argued that their test setup is stiff enough and that the relaxation behavior that they monitored during the tensile testing of Al films is the actual material behavior.

Chasiotis et al., 2007 used the cross-head displacement to study the relaxation in gold thin films. They measured the deformation of the load-cell and the apparatus compliance and subtract it from the results. Due to the high compliance of their specimens compared to the setup, 99% of the cross-head displacement was due to the deformation in the specimen. They verified the accuracy of the crosshead displacement method by testing brittle materials with known elastic modulus.

Greek & Johnson, 1997 cancelled out the effect of the compliance of the test setup by testing specimens with identical gages section areas and different gage lengths. Assuming that the compliance of the test setup is constant for any test, they calculated the deformations caused by test setup and subtract it from the test results. This method is only applicable to the cases that the compliance of the specimens are sufficiently different at different gage lengths.

Emry & Povirk, 2003a also measured the displacement in grippers by monitoring the displacement of two markers using a video camera. They argued that their method has the limitation that the measured strain is not the actual strain in the gage section. They also reported a non-linearity in the stress-strain curve in low loads. Figure 6 shows this nonlinearity which is technically an experimental error. They extrapolated the linear portion of the results to find the zero point of stress-strain curve. Due to this non-linearity in the curve, calculating the yield stress using the 0.2% offset rule was erroneous. Therefore they found the yield point by defining it as the point where the slope of the stress-strain curve drops to one tenth of the elastic modulus.

Due to the uncertainties involved in the application of cross-head displacement for strain measurements, a number of techniques have been introduced to measure the strain directly on the gage section. An inexpensive way of measuring strain is to put markers on the specimen's gage section and monitor their displacement using a camera. Allameh et al., 2004 used a video camera and monitored the deformation of two markers milled by Focused Ion Beam (FIB) on LIGA Ni specimens. Markers were 300μm apart and were located by block matching in a series of images captured by a camera during tensile testing. They have not

Standalone Tensile Testing of Thin Film Materials for MEMS/NEMS Applications 447

optical lever for magnification. They reported that the resolution of the system is limited by

The main advantage of this technique is that since axial and lateral strains can be measured simultaneously, not only Young's modulus but also the Poisson's ratio can be calculated. Since the modulus of the photoresist islands is sufficiently lower than that of the film's, their presence has very negligible effect on the mechanical behavior of the specimen material. The aforementioned techniques were all based on optical imaging. The main issue with imaging techniques is that their resolution is limited by the optical setup, and more specifically by the magnification and the CCD resolution. An advanced method of improving the resolution of optical devices is to use light interference. This approach which is the basis of interferometry techniques has been used by a few researchers for strain

Fig. 7. Double field of view microscope setup for strain measurement (Ogawa et al., 1997) Sharpe et al., 1997 used Interferometric Strain/Displacement Gage (ISDG) method to measure axial and lateral strains in thin film specimens. ISDG was originally proposed by Sharpe (Sharpe, 1968, 1982, 1986, 1989) in the late 1980s to measure strains in macrospecimens in non-contact mode. The principle of this technique is based on the diffraction and interference of light from two slits, i.e. Young's two slit interference. In this method, two markers are put on the specimen. They can be fabricated either by nano-indentation or by FIB-assisted deposition. When the laser beam is illuminated on them the beam is diffracted. The diffracted beams interfere to form interference fringes. The frequency of the fringes is directly proportional to the distance between the two markers. When the specimen is elongated under the applied load, the distance between the two markers varies, resulting in a change in the fringe frequency. By monitoring this frequency the strains can be directly calculated on the specimen. Since the fringe frequency is also affected by the rigid-body motion of the specimen, two separate detectors have to be used to cancel out the effect of

the signal-to-noise ratio of the detector and provides strain resolution of 50μstrains.

measurement in thin film materials.

discussed the accuracy of their setup; however, they reported that the strains that were measured as such were only used in the plastic deformation regime. In this method, one way to achieve higher displacement measurement resolution is to use higher optical magnification. However, at high magnifications, the field of view (FOV) of the objective is so small that the two markers cannot be fit in a single image, simultaneously. To overcome this issue, two different approaches have been used. Cheng et al., 2005 used a low magnification (350X) to fit 180μm-apart markers in a single image. Utilizing the digital image correlation (DIC) method, they post-processed the data to the resolution of 0.02 pixel. For their optical setup, this resolution is the equivalent of 0.01μm displacement on the specimen which translates to 55μstrain resolution for a 180μm gage length. Since compared to other techniques, usually less or no preparation is required on the surface of the specimen and inexpensive optical imaging equipment can be used for this purpose, this method is becoming more popular among researchers. The only disadvantage of DIC is that this method is computationally expensive and therefore cannot be used in real-time and straincontrolled measurements.

In another attempt to tackle the small FOV issue in high magnifications, Ogawa et al., 1997 proposed a double field of view approach. As shown in Figure 7, a low magnification objective is used to view the two markers which were 1-1.4mm apart. Image of each marker position was then magnified on a separate CCD and their displacement was monitored. In their technique, they could measure displacements to better than 1μm corresponding to 0.1% strain for a 1mm gage length.

Fig. 6. Stress-strain curve of gold thin films, showing non-linearity at low loads. The dashed line is fitted to the curve to find the zero point. (Emry & Povirk, 2003a)

Ruud et al., 1993 patterned a two-dimensional area of photoresist islands on the specimen and monitored the displacement of the diffracted spots from these islands to directly measure the strain on the gage section. As shown in Figure 8, presence of the photoresist islands results in diffraction patterns when a laser beam is illuminated on the surface of the sample. Diffracted spots are then detected using a two-dimensional position sensor. By monitoring the displacement of these spots, the relative displacement of the islands and hence the specimen deformation can be measured. In this setup, system works in the third diffraction order and the distance between the sample and position detector serves as an

discussed the accuracy of their setup; however, they reported that the strains that were measured as such were only used in the plastic deformation regime. In this method, one way to achieve higher displacement measurement resolution is to use higher optical magnification. However, at high magnifications, the field of view (FOV) of the objective is so small that the two markers cannot be fit in a single image, simultaneously. To overcome this issue, two different approaches have been used. Cheng et al., 2005 used a low magnification (350X) to fit 180μm-apart markers in a single image. Utilizing the digital image correlation (DIC) method, they post-processed the data to the resolution of 0.02 pixel. For their optical setup, this resolution is the equivalent of 0.01μm displacement on the specimen which translates to 55μstrain resolution for a 180μm gage length. Since compared to other techniques, usually less or no preparation is required on the surface of the specimen and inexpensive optical imaging equipment can be used for this purpose, this method is becoming more popular among researchers. The only disadvantage of DIC is that this method is computationally expensive and therefore cannot be used in real-time and strain-

In another attempt to tackle the small FOV issue in high magnifications, Ogawa et al., 1997 proposed a double field of view approach. As shown in Figure 7, a low magnification objective is used to view the two markers which were 1-1.4mm apart. Image of each marker position was then magnified on a separate CCD and their displacement was monitored. In their technique, they could measure displacements to better than 1μm corresponding to

Fig. 6. Stress-strain curve of gold thin films, showing non-linearity at low loads. The dashed

Ruud et al., 1993 patterned a two-dimensional area of photoresist islands on the specimen and monitored the displacement of the diffracted spots from these islands to directly measure the strain on the gage section. As shown in Figure 8, presence of the photoresist islands results in diffraction patterns when a laser beam is illuminated on the surface of the sample. Diffracted spots are then detected using a two-dimensional position sensor. By monitoring the displacement of these spots, the relative displacement of the islands and hence the specimen deformation can be measured. In this setup, system works in the third diffraction order and the distance between the sample and position detector serves as an

line is fitted to the curve to find the zero point. (Emry & Povirk, 2003a)

controlled measurements.

0.1% strain for a 1mm gage length.

optical lever for magnification. They reported that the resolution of the system is limited by the signal-to-noise ratio of the detector and provides strain resolution of 50μstrains.

The main advantage of this technique is that since axial and lateral strains can be measured simultaneously, not only Young's modulus but also the Poisson's ratio can be calculated. Since the modulus of the photoresist islands is sufficiently lower than that of the film's, their presence has very negligible effect on the mechanical behavior of the specimen material.

The aforementioned techniques were all based on optical imaging. The main issue with imaging techniques is that their resolution is limited by the optical setup, and more specifically by the magnification and the CCD resolution. An advanced method of improving the resolution of optical devices is to use light interference. This approach which is the basis of interferometry techniques has been used by a few researchers for strain measurement in thin film materials.

Fig. 7. Double field of view microscope setup for strain measurement (Ogawa et al., 1997)

Sharpe et al., 1997 used Interferometric Strain/Displacement Gage (ISDG) method to measure axial and lateral strains in thin film specimens. ISDG was originally proposed by Sharpe (Sharpe, 1968, 1982, 1986, 1989) in the late 1980s to measure strains in macrospecimens in non-contact mode. The principle of this technique is based on the diffraction and interference of light from two slits, i.e. Young's two slit interference. In this method, two markers are put on the specimen. They can be fabricated either by nano-indentation or by FIB-assisted deposition. When the laser beam is illuminated on them the beam is diffracted. The diffracted beams interfere to form interference fringes. The frequency of the fringes is directly proportional to the distance between the two markers. When the specimen is elongated under the applied load, the distance between the two markers varies, resulting in a change in the fringe frequency. By monitoring this frequency the strains can be directly calculated on the specimen. Since the fringe frequency is also affected by the rigid-body motion of the specimen, two separate detectors have to be used to cancel out the effect of

Standalone Tensile Testing of Thin Film Materials for MEMS/NEMS Applications 449

In another effort to use interferometric measurement techniques, Read, 1998 used speckle interferometry to measure in-plane strains in thin film specimens. The main advantage of speckle interferometry is that since it uses the speckles caused by the surface topography, no surface preparation or marker fabrication is required. However, it is usually computationally expensive and has low signal-to-noise ratio. In this technique, instead of the strain, the strain rate was measured in the elastic deformation regime and was used to calculate the modulus of elasticity. The uncertainty of the calculated modulus was reported

Tajik, 2008 used another interferometric technique to measure the strain fields in a thin film specimen. This method is schematically represented in Figure 10-a. Diffraction gratings are milled on the freestanding thin film specimen using Focused Ion Beam (FIB). (Figure 10-b and c) Gratings are then illuminated by two laser beams and the interferogram thus formed is captured via a CCD camera. Deformation of the specimen and hence the gratings will result in changes in the interferogram. Intensity of the interferogram can be correlated to the

> <sup>0</sup> ( , ) ( , ) ( , )cos(2 (2 ) ( , )) *<sup>s</sup> Ixy I xy xy f Uxy*

intensity and fringe visibility, respectively. In this equation, *sf* is the spatial frequency of

As shown in Equation (1), displacement field is essentially the phase of the interferogram. Therefore, in order to measure displacement field, one needs to calculate the phase value from the interferogram data. For this purpose, continuous wavelet transformation (CWT) has been used in this study. In brief, it has been shown that the spatial derivative of the displacement field, which in fact corresponds to strains, correlates with the value of the

> <sup>1</sup> ( ) 2 () *<sup>c</sup> xx*

where ( ) *<sup>r</sup> a x* is the scale value on the ridge of the wavelet for any coordinate *x* and *cf* is the center frequency of the Morlet wavelet. This method is then used to extract uniform and non-uniform strain fields. It is shown that wavelet transformations have exceptional capabilities in denoising the experimental interferogram, given appropriate wavelet parameters are chosen in the analysis. Figure 11 demonstrates the capabilities of this method to reconstruct the non-uniform strain field around a hole in a plate under axial tension. The last group of strain measurement methods are those that used advanced microscopy techniques to measure the strain in thin films. The challenges involved in using optical microscopy led researchers to use other microscopy techniques like AFM, SEM, and TEM to measure the deformation of thin films specimens. These techniques, on the other hand, can provide an insight into the microstructural deformation of thin film materials during

Chasiotis & Knauss, 2002 monitored the surface topography changes during loading using Atomic Force Microscopy (AFM). Correlating the AFM images of the deformed and undeformed surface using Digital Image Correlation (DIC), they calculated the strain field.

*s r <sup>f</sup> <sup>x</sup> f a x*

where *Ixy* (,) is the interferogram intensity, and 0*I x*(,) *y* and

scaling parameter at the ridge of the transformation,

the gratings and *U x*(,) *y* represents in the axial displacement field.

(1)

(,) *x y* are the background

(2)

to be 5%.

loading.

displacement field, such that

this motion. A schematic of this setup is shown in Figure 9. In the original setup, in order to measure the strains from the fringe data, the location of the fringe minimum was isolated at the beginning of the test and was followed through a complex algorithm. In this algorithm only a small part of the optical signal was used and most of it which contained a lot of information was omitted in calculations. With this algorithm, the strain resolution was 5μstains with uncertainty of ±30μstrains. Zupan & Hemker, 2002 used Fourier Transforms on the whole optical signal and improved the uncertainty of the technique to ±15μstrains. An advantage of ISDG is that if markers are placed along the width of the specimen, the lateral strains and hence the Poisson's ratio can also be measured with this technique. However, since the markers have to be at least 300μm apart, (Hemker & Sharpe, 2007) wide specimens have to be utilized.

Fig. 8. Schematic diagram of the setup to use diffraction spots for strain measurement (Ruud et al., 1993)

Fig. 9. Schematic representation of ISDG technique. (Sharpe et al., 1997)

this motion. A schematic of this setup is shown in Figure 9. In the original setup, in order to measure the strains from the fringe data, the location of the fringe minimum was isolated at the beginning of the test and was followed through a complex algorithm. In this algorithm only a small part of the optical signal was used and most of it which contained a lot of information was omitted in calculations. With this algorithm, the strain resolution was 5μstains with uncertainty of ±30μstrains. Zupan & Hemker, 2002 used Fourier Transforms on the whole optical signal and improved the uncertainty of the technique to ±15μstrains. An advantage of ISDG is that if markers are placed along the width of the specimen, the lateral strains and hence the Poisson's ratio can also be measured with this technique. However, since the markers have to be at least 300μm apart, (Hemker & Sharpe, 2007) wide

Fig. 8. Schematic diagram of the setup to use diffraction spots for strain measurement

Fig. 9. Schematic representation of ISDG technique. (Sharpe et al., 1997)

specimens have to be utilized.

(Ruud et al., 1993)

In another effort to use interferometric measurement techniques, Read, 1998 used speckle interferometry to measure in-plane strains in thin film specimens. The main advantage of speckle interferometry is that since it uses the speckles caused by the surface topography, no surface preparation or marker fabrication is required. However, it is usually computationally expensive and has low signal-to-noise ratio. In this technique, instead of the strain, the strain rate was measured in the elastic deformation regime and was used to calculate the modulus of elasticity. The uncertainty of the calculated modulus was reported to be 5%.

Tajik, 2008 used another interferometric technique to measure the strain fields in a thin film specimen. This method is schematically represented in Figure 10-a. Diffraction gratings are milled on the freestanding thin film specimen using Focused Ion Beam (FIB). (Figure 10-b and c) Gratings are then illuminated by two laser beams and the interferogram thus formed is captured via a CCD camera. Deformation of the specimen and hence the gratings will result in changes in the interferogram. Intensity of the interferogram can be correlated to the displacement field, such that

$$I(\mathbf{x}, y) = I\_0(\mathbf{x}, y) + \varphi(\mathbf{x}, y) \cos(2\pi(2f\_s) \mathcal{U}(\mathbf{x}, y)) \tag{1}$$

where *Ixy* (,) is the interferogram intensity, and 0*I x*(,) *y* and (,) *x y* are the background intensity and fringe visibility, respectively. In this equation, *sf* is the spatial frequency of the gratings and *U x*(,) *y* represents in the axial displacement field.

As shown in Equation (1), displacement field is essentially the phase of the interferogram. Therefore, in order to measure displacement field, one needs to calculate the phase value from the interferogram data. For this purpose, continuous wavelet transformation (CWT) has been used in this study. In brief, it has been shown that the spatial derivative of the displacement field, which in fact corresponds to strains, correlates with the value of the scaling parameter at the ridge of the transformation,

$$
\varepsilon\_{\rm xx}(\mathbf{x}) = \frac{1}{2f\_s} \frac{f\_c}{a\_r(\mathbf{x})} \tag{2}
$$

where ( ) *<sup>r</sup> a x* is the scale value on the ridge of the wavelet for any coordinate *x* and *cf* is the center frequency of the Morlet wavelet. This method is then used to extract uniform and non-uniform strain fields. It is shown that wavelet transformations have exceptional capabilities in denoising the experimental interferogram, given appropriate wavelet parameters are chosen in the analysis. Figure 11 demonstrates the capabilities of this method to reconstruct the non-uniform strain field around a hole in a plate under axial tension.

The last group of strain measurement methods are those that used advanced microscopy techniques to measure the strain in thin films. The challenges involved in using optical microscopy led researchers to use other microscopy techniques like AFM, SEM, and TEM to measure the deformation of thin films specimens. These techniques, on the other hand, can provide an insight into the microstructural deformation of thin film materials during loading.

Chasiotis & Knauss, 2002 monitored the surface topography changes during loading using Atomic Force Microscopy (AFM). Correlating the AFM images of the deformed and undeformed surface using Digital Image Correlation (DIC), they calculated the strain field.

Standalone Tensile Testing of Thin Film Materials for MEMS/NEMS Applications 451

nanostructures rather than common thin film materials. A stress-strain curve along with respective microstructural observations produced by this method is shown in Figure 13.

(a) (b)

0 0.5 1 1.5 2 2.5 3 x 10-3

0 0.2 0.4 0.6 0.8 1 1.2 1.4 x 10-4

xx (Strains)

xx (Strains)

(c)


Original Reconstructed

x (m)

Original Reconstructed


x (m)

Fig. 11. (a) Reconstructed (top) and original (bottom) strain field using continuous wavelet transformations, (b) reconstructed strains at top of the hole (y=12μm), (c) through the hole

Fig. 12. Displacement field in the vicinity of a crack in polysilicon film measured by

(y=0). (Tajik, 2008)

AFM/DIC. (Chasiotis, 2004)

The process of imaging is very time intensive and usually takes about 10 minutes for each scan and is confined to an area of a few microns long. In addition to the time required for each AFM scan, there is also the post-processing time added for DIC. They reported 400 μstrains resolution in their strain measurements for a 512×512 pixel image and 1/8 pixel DIC resolution. However, the main advantage of this technique is that it provides a wholefield strain data which helped the analysis of the strain field around geometry inclusions and notches (Chasiotis & Knauss, 2003), as well as cracks. (Chasiotis et al., 2006; Cho et al., 2007). A typical displacement field at the vicinity of a crack in polysilicon that has been measured using AFM/DIC is shown in Figure 12.

Fig. 10. (a) Schematic representation of the optical setup for moiré interferometry, (b) diffraction gratings fabricated using FIB milling on the test specimen, and (c) high magnification image of the gratings on the specimen. (Tajik, 2008)

A few researchers used MEMS based devices to study the mechanical properties of thin films in electron microscopes. If the thin film samples are electron transparent, i.e. have nanometer thickness, *in situ* studies in TEM are also possible which provides more information on the microstructural deformations during loading. Haque & Saif, 2003, 2004 used the technique to study the mechanical behavior of Al and Au thin film specimens under SEM and TEM. The resolution of the measured strain and stress depends on the magnification of the microscope and the size of the specimen. At 100nm microscope resolution, the strain resolution was 0.05% for 200nm thick and 185μm long Al films and was 0.03% for 100nm thick and 275μm long specimens. Rajagopalan et al., 2007 reported lower strain resolutions of 0.005% and 0.01% for Al and Au films, respectively. Although this method of strain measurement has a high resolution and provides extra information on the microstructural deformations, its force and displacement scales are within the limits of

The process of imaging is very time intensive and usually takes about 10 minutes for each scan and is confined to an area of a few microns long. In addition to the time required for each AFM scan, there is also the post-processing time added for DIC. They reported 400 μstrains resolution in their strain measurements for a 512×512 pixel image and 1/8 pixel DIC resolution. However, the main advantage of this technique is that it provides a wholefield strain data which helped the analysis of the strain field around geometry inclusions and notches (Chasiotis & Knauss, 2003), as well as cracks. (Chasiotis et al., 2006; Cho et al., 2007). A typical displacement field at the vicinity of a crack in polysilicon that has been

Fig. 10. (a) Schematic representation of the optical setup for moiré interferometry, (b) diffraction gratings fabricated using FIB milling on the test specimen, and (c) high magnification image of the gratings on the specimen. (Tajik, 2008)

A few researchers used MEMS based devices to study the mechanical properties of thin films in electron microscopes. If the thin film samples are electron transparent, i.e. have nanometer thickness, *in situ* studies in TEM are also possible which provides more information on the microstructural deformations during loading. Haque & Saif, 2003, 2004 used the technique to study the mechanical behavior of Al and Au thin film specimens under SEM and TEM. The resolution of the measured strain and stress depends on the magnification of the microscope and the size of the specimen. At 100nm microscope resolution, the strain resolution was 0.05% for 200nm thick and 185μm long Al films and was 0.03% for 100nm thick and 275μm long specimens. Rajagopalan et al., 2007 reported lower strain resolutions of 0.005% and 0.01% for Al and Au films, respectively. Although this method of strain measurement has a high resolution and provides extra information on the microstructural deformations, its force and displacement scales are within the limits of

(c)

measured using AFM/DIC is shown in Figure 12.

(a) (b)

nanostructures rather than common thin film materials. A stress-strain curve along with respective microstructural observations produced by this method is shown in Figure 13.

Fig. 11. (a) Reconstructed (top) and original (bottom) strain field using continuous wavelet transformations, (b) reconstructed strains at top of the hole (y=12μm), (c) through the hole (y=0). (Tajik, 2008)

Fig. 12. Displacement field in the vicinity of a crack in polysilicon film measured by AFM/DIC. (Chasiotis, 2004)

Standalone Tensile Testing of Thin Film Materials for MEMS/NEMS Applications 453

interferometry have much higher resolution and can be used to extract strain values as well as strain fields. However, their main disadvantage is the hardware complexity and cost. On the other hand, optical imaging methods in combination with Digital Image Correlation (DIC) can provide about the same resolution; however, they are computationally expensive and cannot be used in real-time and strain-controlled experiments. Therefore, depending on the specific type of application, one needs to

The information obtain through this review provide a detailed understanding of the challenges involved in tensile testing of thin film materials and different approaches that were used to tackled these issues. The results will help design and implement a device that can meet these challenges toward a reliable and precise study of the mechanical

The financial support from the Natural Sciences and Engineering Council of Canada (NSERC) is appreciated. Center for Integrated RF Engineering (CIRFE) and WatLabs of the University of Waterloo, Nanofabrication Laboratory of the University of Western Ontario and the Canadian Centre for Electron Microscopy in McMaster University are acknowledged for providing research facilities. A great portion of this research is conducted in Laboratory for the Mechanical Properties of Thin Film Materials at the University of

Allameh, S. M. (2003). An introduction to mechanical properties related issues in MEMS

Allameh, S. M., Lou, J., Kavishe, F., Buchheir, T., & Soboyejo, W. O. (2004). An investigation

Born, M., & Wolf, E. (1983). Principles of Optics: Electromagnetic Theory of Propagation,

Buchheit, T. E., Glass, S. J., Sullivan, J. R., Mani, S. S., Lavan, D. A., Friedmann, T. a., & Janek,

Chassiotis, I., & Knauss, W. G. (2002). A new microtensile tester for the study of MEMS

Chasiotis, I., & Knauss, W. G. (2003a). The mechanical strength of polysilicon films: Part 1.

Chasiotis, I., & Knauss, W. G. (2003b). The mechanical strength of polysilicon films: Part 2.

of fatigue in LIGA Ni MEMS thin films, *Materials Science and Engineering A*, Vol.

Interference, and Diffraction of Light, Cambridge University Press, ISBN

R., (2003). Micromechanical testing of MEMS materials, *Journal of Materials Science*,

materials with the aid of Atomic Force Microscopy, *Experimental Mechanics*, Vol. 42,

The influence of fabrication governed surface conditions, *Journal of the Mechanics* 

Size effects associated with elliptical and circular perforations, *Journal of the* 

structures, *Journal of Materials Science*, Vol. 38, pp. 4115-4123.

choose either method to measure strains or strain fields across the gage length.

behavior of thin film materials.

**9. Acknowledgment** 

Waterloo.

**10. References** 

371, pp. 256-266.

0521642221, Cambridge, UK.

*and Physics of Solids*, Vol. 51, pp. 1533-1550.

*Mechanics and Physics of Solids*, Vol. 51, pp. 1551-1572.

Vol. 38, pp. 4081-4086.

No. 1, pp. 51-57.

Fig. 13. *In situ* TEM test results for Al thin film specimens. Microstructural deformations corresponding to the tensile test is also presented. (Haque & Saif, 2004)
