In situ high temperature creep deformation of micro ... - Semantic Scholar
Microelectronics Reliability 53 (2013) 652–657
Contents lists available at SciVerse ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel
In situ high temperature creep deformation of micro-structure with metal film wire on flexible membrane using geometric phase analysis Qinghua Wang a,b, Satoshi Kishimoto a, Huimin Xie b,⇑, Zhanwei Liu c, Xinhao Lou c a
National Institute for Materials Science, Tsukuba, 305-0047 Ibaraki, Japan AML, Department of Engineering Mechanics, Tsinghua University, 100084 Beijing, China c School of Aerospace Engineering, Beijing Institute of Technology, 100081 Beijing, China b
a r t i c l e
i n f o
Article history: Received 8 July 2012 Received in revised form 5 October 2012 Accepted 23 October 2012 Available online 8 December 2012
a b s t r a c t A way of measuring the in situ high temperature creep deformation of a micro-structure with a metal film wire on a flexible membrane is developed. The creep deformation measurement of a micro-structure with a Karma alloy wire on a polyimide membrane is used as an application. High temperature gratings were fabricated directly on the surfaces of two Karma alloy wires using the focused ion beam milling technique after the grating frequencies were designed. The grating morphologies with different isothermal soaking time were recorded by a scanning electron microscope with a heating apparatus. The in situ high temperature creep deformations in a micro-region of the structure were measured by performing the geometric phase analysis. The creep behaviors of this structure at 300 °C and 500 °C were analyzed. The developed measurement method is prospective in evaluating the reliability of the film-wire/substrate structures at a high temperature. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The structures composed of metal film wires and flexible substrates have been extensively adopted in the semiconductor integrated circuits, micro–electro-mechanical systems, and flexible electronic devices [1,2]. With the development of miniaturization and integration, the characteristic dimension of metal film wires has reached the micron and submicron levels [3]. During the application process, the film-wire/substrate structures are usually employed in high temperature environments. The stability of a structure at a high temperature is closely related to its creep behavior. However, the complexity of a film-wire/substrate structure makes it very difficult to investigate the high temperature deformation of the structure. To our knowledge, few reports study the deformation of a micro-structure with a metal film wire on a flexible substrate at a high temperature. In this study, we attempt to develop a measurement method to explore the in situ high temperature creep deformation of a micro-film-wire/substrate structure, and a structure with a Karma alloy wire on a polyimide membrane is used to illustrate this method. A speckle pattern and a grating pattern are two basic deformation carriers in optical methods. In general, the surface topography of a deformation carrier on a metal film wire at the micrometer scale is observed using a high power microscope. A speckle pattern
⇑ Corresponding author. E-mail address: [email protected] (H. Xie). 0026-2714/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.microrel.2012.10.016
is often used in the digital image correlation (DIC) method [4,5]. However, the brightness and the contrast of a speckle pattern need to be frequently adjusted at a high temperature in a scanning electron microscope (SEM), which limits the application of the DIC method on the high temperature deformation measurement of a micro-structure. A grating pattern is a basic component in moiré methods [6,7] and the geometric phase analysis (GPA) technique [8,9], which are not affected by the brightness and the contrast of the grating pattern in a SEM. As a consequence, a high temperature grating becomes a good choice to analyze the high temperature creep deformation of a micro-structure [10]. Common micro-grating fabrication techniques include photolithography, electron beam lithography, nanoimprint lithography, atomic force microscope ruling and focused ion beam (FIB) milling. Photolithography such as the holographic interferometry lithography technique is able to generate gratings with frequencies up to several thousands of lines per millimeter [11]. Electron beam lithography is reported to be capable of fabricating a 10,000 lines/mm grating on a silicon wafer [12]. Nanoimprint lithography provides an easy way to produce micro- and nano-gratings [13]. However, photoresists are necessary in the above three techniques, and high-temperature photoresists are very expensive. The atomic force microscope ruling method can be utilized to fabricate a grating with a frequency of tens of thousands of lines per millimeter [14]. Nevertheless, the concave–convex structure with a film wire on a substrate is likely to damage an atomic force microscope probe. The FIB milling technique without the need for photoresist is known as a powerful micro-machining tool, having many advantages such
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653
as high resolution, convenient location and high milling speed [15–17]. Based on the FIB milling technique, high temperature micro-gratings can be fabricated on the surface of a Karma alloy wire on a polyimide membrane. To investigate the in situ creep deformation of a microfilm-wire/substrate structure, a SEM with a heating apparatus is used both for heating and observation in this study. Because the movement of the sample stage of the SEM with a heating apparatus cannot be quantitatively controlled, it is hard to apply the phase shifting SEM moiré method which can improve the measurement accuracy of the SEM moiré method. Fortunately, the GPA technique with a high measurement accuracy [18], which can directly analyze the grating images, provides a feasible way to determine the sample deformation in a SEM with a heating apparatus. After the grating frequencies are designed according to the structure size and the SEM condition, the creep deformations of the structure with a Karma alloy on a polymer membrane are investigated in this study. Fig. 1. Sample morphology and the sketch map of the structure.
2. Principle of geometric phase analysis GPA is able to obtain the deformation information from calculating the local Fourier components of lattice fringes [18]. If an image includes a grating with a frequency of f ðrÞ and the displacement is uðrÞ after deformation, the displacement is directly related to the phase difference DP f ðrÞ of the image [18,19]:
uðrÞ ¼
DPf ðrÞ 2pf ðrÞ
ð1Þ
The strain can be obtained from the first derivative of the displacement. For instance, if there are two frequencies (f1 and f 2 ) in an image, the displacement and the strain components can be expressed by:
ux uy
¼
exx exy eyx eyy
1 2p
¼
f1x
f1y
f2x
f2y
1 2p
1
P f1
ð2Þ
P f2
f1x
f1y
f2x
f2y
1
@Pf1 =@x @Pf1 =@y @Pf2 =@x @Pf2 =@y
ð3Þ
where ux ; uy indicate the displacement components in the X, Y directions, respectively, exx ; eyy ; exy express the strain components in the X, Y directions as well as the shearing strain, respectively, f1x ; f1y ; f2x ; f2y are the frequency components in the X, Y directions, respectively, and Pf 1 ; Pf 2 represent the phases corresponding to f1 ; f2 , respectively [20]. As long as the grating images before and after deformation are recorded, the displacement and the corresponding strain will be able to be obtained from the GPA technique. 3. Experimental details 3.1. Sample preparation The sample consists of a Karma alloy wire and a polyimide (PI) membrane, which is fabricated by photolithography. The Karma alloy wire is distributed in a sequential narrow ‘S’ shape. The Karma alloy contains 73% nickel, 20% chromium, and a small quantity of aluminum, iron and manganese. Due to excellent performances, the Karma alloy is widely used as a main component of a resistance strain gauge working in high temperature or low temperature environments. The PI membrane commonly serves as a flexible substrate, which has extensive applications in flexible electronic devices such as flexible screens, electronic papers and artificial skins.
The morphology and the structure of the sample are illustrated in Fig. 1. The thickness, the width and the length of the Karma alloy wire are 4 lm, 66 lm and 10 mm, respectively. The spacing between two adjacent segments of the Karma alloy wire is 134 lm. The thickness, the width and the length of the whole PI membrane are 30 lm, 6 mm and 16 mm, respectively. 3.2. Micro-grating design and fabrication To perform the GPA, a grating is necessary to be fabricated on the surface of the Karma alloy wire. If the grating frequency is too low, the accuracy of deformation measurement will not meet the requirement. On the other hand, if the grating frequency is too high, the grating region will be very small, the FIB milling time will be very long and the grating quality will be poor due to the unsmooth surface of the Karma alloy wire. Even if a grating with a little better quality could be fabricated, it is very hard to obtain a clear grating image, because the magnification of a SEM with a heating apparatus is limited within 2000. The higher the temperature is, the harder the SEM imaging becomes, and only the image of a lower-frequency grating can be clear when the temperature reaches 500 °C. We have carried out some experiments and found that it is appropriate when the grating frequency is in the range of 1000–2500 lines/mm. Two cross gratings with frequencies of 2000 lines/mm and 1000 lines/mm are chosen to be fabricated on the Karma alloy wire surfaces of two samples, respectively. Sample 1# with the 2000 lines/mm grating is used to investigate the creep behavior of the sample in a micro-region at 300 °C, and sample 2# with the 1000 lines/mm grating is aimed at the creep behavior at 500 °C. The sample stage is tilted at 50°, the accelerating voltage of the ion beam is set to be 30 kV and the free working distance is 18 mm when the two gratings are fabricated in a FIB system. The axial direction of the Karma alloy wire should be adjusted to be parallel or perpendicular to the horizontal direction before grating fabrication. As a result, the two principle directions of the cross grating will be parallel and perpendicular to the axis direction of the Karma alloy wire, respectively. The choice of a cross grating over a one-way grating is to eliminate the calculation error when the principle direction of the one-way grating is not exactly parallel to the wire axial direction. The SEM images of the cross grating with a frequency of 2000 lines/mm on sample 1# are displayed in Fig. 2. The enlarged view (Fig. 2a) and the global view (Fig. 2b) of the grating show the grating topography and the location of the grating region,
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Q. Wang et al. / Microelectronics Reliability 53 (2013) 652–657
(a) enlarged view
(b) global view
Fig. 2. SEM images of the cross grating with a frequency of 2000 lines/mm fabricated by FIB on the surface of the Karma alloy wire of sample 1#.
respectively. The depth of the grating is 0.2 lm, less than one-tenth of the thickness of the Karma alloy wire (4 lm). Therefore, the effect of the grating on the Karma alloy wire is negligible. The width and the length of the grating region are 50 lm and 100 lm, respectively. Only a part of the grating region is observed during the heating process in a SEM. The SEM images of the 1000 lines/mm grating on sample 2# are shown in Fig. 3. Because this grating will be used at 500 °C, the grating depth must be larger enough to ensure clear grating images recorded by a SEM. The grating depth is set to be 0.4 lm, one-tenth of the thickness of the Karma alloy wire. The width and the length of the grating region are 26 lm and 80 lm, respectively, where the width is less than half of the wire width. Consequently, the influence of the 1000 lines/mm grating on the Karma alloy wire can also be ignored. 3.3. High temperature creep experiments A Shimadzu SEM with a heating apparatus is utilized to carry out the experiments of heating, isothermal soaking and observation of the samples (Fig. 4a). To avoid the crimping of the PI membrane at a high temperature, the sample with the Karma alloy wire on the polyimide membrane should be fixed on a rigid substrate.
(a) enlarged view
According to the shape and the dimensions of the standard tensile specimen of this SEM, a dumbbell sample base made from SUS304 stainless steel (SS) is fabricated, as seen in Fig. 4b. The thickness of the SS base is 1 mm. After the marginal regions of a sample made up of the Karma alloy wire and the PI membrane are cut, the two ends of the sample are pasted on the surface of the SS base by high temperature glue. It should be noted that the grating region on the sample should be placed in the central region along the length of the SS base. So that the grating images can be recorded from the observation window of the SEM during the heating and the isothermal soaking processes. A pre-tensile load of 0.03 kN is exerted on the SS base in the SEM before heating. To avoid the shift of the SS base, the preload is kept unchanged during the processes of heating and isothermal soaking. The heating rate of the heating apparatus in the SEM is set to be 20 °C/min. Before the grating images are recorded, we should make sure that the axis of the Karma alloy wire is parallel to the vertical or the horizontal direction and the grating images fill the entire screen. Sample 1# with the 2000 lines/mm grating is kept at 300 °C for 240 min to study its micro-region creep behavior. The grating images are recorded every 60 min at the beginning, and every 30 min two hours later. Sample 2# with the 1000 lines/mm grating
(b) global view
Fig. 3. SEM images of the cross grating with a frequency of 1000 lines/mm fabricated by FIB on the surface of the Karma alloy wire of sample 2#.
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duced by the creep deformation are displayed in Fig. 5b and c, respectively. The strain distribution is calculated by Eq. (3), and the average strain along the wire axis is e = 0.0226. Using the same calculation process, the micro-region creep deformations of the samples at 300 °C and 500 °C at different isothermal soaking time are acquired by GPA. The relationships between the micro-region creep strain and the isothermal soaking time of the samples at 300 °C and 500 °C are plotted in Figs. 6 and 7, respectively. All the micro-region creep strains are compressive, and the absolute value of strain increases with the increasing isothermal soaking time. The maximal absolute value of the microregion creep strain at 300 °C is 0.0171, and the maximal value reaches 0.0347 at 500 °C.
Electron beam
Grating Karma alloy
PI SUS304
4.2. Discussion
Heating apparatus in SEM
(a) Experimental setup
SUS304
(b) Size of a standard tensile specimen with a thickness of 1mm (Unit: mm) Fig. 4. Schematic diagram of the experimental setup and the standard tensile specimen under a Shimadzu SEM with a heating apparatus, in which the red line expresses the high temperature glue and the pink rectangle stands for the sample. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
is kept at 500 °C for 300 min, and the grating images are collected at intervals of 60 min. 4. Results and discussion 4.1. Creep deformation measurement The grating images at 300 °C and 500 °C before the isothermal soaking process (zero time) are treated as the reference grating images. The distributions of the phase differences and the displacements of the grating images at different isothermal soaking time can be calculated by GPA. The corresponding strain fields will then be obtained from the partial derivatives of the displacement fields. The average value of a strain field is just the micro-region strain at this moment. When the strain ranges from 1 105 to 1 101, the calculated strain error is less than 5% [21]. The creep deformation of the structure with the Karma alloy wire on the PI membrane along the wire axis is mainly concerned. Taking sample 2# at 500 °C for 60 min as an example, the calculation process of GPA for the deformation will be presented. The 1000 lines/mm grating at 500 °C before the isothermal soaking process is considered as the reference image. Fig. 5a shows the calculation area on the sample surface. The distributions of the phase difference and the displacement of sample 2# at this moment in-
During the processes of heating and isothermal soaking, four layers of the structure, i.e., the Karma alloy wire, the PI membrane, the high temperature glue and the SUS304 SS base, interact with each other. The corresponding material constants are listed in Table 1. It is clear that the thickness of the SS base is much greater than those of the other three layers, and (EA)SS (EA)karma, (EA)SS (EA)PI, (EA)SS (EA)glue, where E, A represent the Young’s modulus and the cross sectional area respectively. Consequently, we can suppose that the SS base is free to undergo thermal expansion as if the other three layers do not exist. The locations of the Karma alloy wire, the PI membrane and the high temperature glue are determined by the SS base. In consideration of the slender characteristics, it is assumed that the Karma alloy wire, the PI membrane and the SS base experience linear expansion only along the length direction. When the environmental temperature in the SEM rises from the room temperature to a high temperature, a pre-tensile stress will exist in the Karma alloy wire because the thermal expansion coefficient (TEC) of the Karma alloy is smaller than that of SS, and a pre-compressive stress will exist in the PI membrane as the TEC of PI is greater than that of SS. The effect of the small pre-tensile load of the SS base on the deformation of the composite structure is ignored in the above analysis. The two parts of the high temperature glue will expand along their length directions which are perpendicular to the axial direction of the SS base, as seen from Fig. 4b. Due to the greater TEC of the high temperature glue compared with the SS base, there will be pre-compressive stress in the glue. However, the pre-compressive stresses and the creep deformations of the two parts of the glue will not affect the deformation of the composite structure of the Karma alloy wire and the PI membrane, because the length directions of the glue parts are perpendicular to the length direction of the composite structure. As we all know, the creep temperature of a polymer material is higher than its glass transition temperature (GTT), and the creep temperature of a metal is greater than 0.3–0.4Tm, where Tm is the thermodynamic melting point. According to the data in Table 1, the creep temperatures of the PI membrane, the Karma alloy wire and the SS base are 280 °C, 214–376 °C, 232– 400 °C respectively. At 300 °C, the PI membrane has begun to creep, but the Karma alloy wire and the SUS304 SS base have not yet entered or are just beginning to enter the creep range. Due to the pre-compressive stress in the PI membrane, a compressive deformation occurs in the micro-region in the PI membrane during the creep process. The Karma alloy wire on the PI membrane will also get a compressive deformation. This is the reason why the micro-region creep strain in Fig. 6 is negative. The creep deformation of the high temperature glue in the width direction of the SS base and the unchanged preload of the SS base during the isothermal soaking
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Q. Wang et al. / Microelectronics Reliability 53 (2013) 652–657
(a) calculation area
(c) displacement (0.076 m/pixel)
(b) unwrapped phase
Fig. 5. Micro-region creep deformation of the structure with the Karma alloy wire on the PI membrane at 500 °C for 60 min.
Table 1 Material constants of the Karma alloy wire, the PI membrane, the high temperature glue and the SUS304 SS base, where GTT is glass transition temperature and TEC is thermal expansion coefficient.
Fig. 6. Variation of the micro-region creep strain of the structure with the Karma alloy wire on the PI membrane along with the isothermal soaking time at 300 °C.
Material
Young’s modulus E (GPa)
Thickness h (lm)
TEC a (106 K)
GTT or melting point (°C)
PI Glue Karma alloy SS
2.0 3.6 210
30 33 4
30 80–110 11.8
193
1000
17.3
280 (GTT) – 1350 (melting) [22] 1410 (melting)
At 500 °C, all the four materials have entered the creep stage. The absolute value of the micro-region creep deformation of the PI membrane (polymer) is greater than that of the Karma alloy wire and the SUS304 SS base (metals). Finally, a compressive deformation appears in the micro-region of the structure with the Karma alloy wire on the PI membrane owing to the compatibility of deformation (Fig. 7). 5. Conclusion
Fig. 7. Variation of the micro-region creep strain of the structure with the Karma alloy wire on the PI membrane along with the isothermal soaking time at 500 °C.
process will not influence the creep deformation of the composite structure. The absolute values of the micro-region creep strain along with the isothermal soaking time in Fig. 6 indicate that the PI membrane has a poor resistance to the creep deformation at 300 °C. It is generally thought that the PI membrane can work for a long term in the environment of 260 to 300 °C. However, greater micro-region creep strain of the PI membrane will arise at 300 °C under long isothermal soaking time from this study. It suggests that the PI membrane is not suitable for a long-term use for micro-analysis at 300 °C.
In this study, an approach based on the FIB milling technique and geometric phase analysis is developed to study the in situ high temperature creep behavior of a micro-structure with a metal film wire on a flexible membrane. The in situ high temperature creep deformation of the micro-structure with a Karma alloy wire on a polyimide membrane is investigated. Two high temperature cross gratings are designed and successfully fabricated on two samples. Gratings with frequencies of 2000 lines/ mm and 1000 lines/mm are used at 300 °C and 500 °C in a SEM with a heating apparatus, respectively. The in situ high temperature creep deformations in micro-regions of the samples are measured and analyzed taking advantage of geometric phase analysis. This work provides a simple and effective way to investigate the in situ high temperature creep behaviors of the filmwire/substrate structures. The approach described in this study has a good potential to assess the stability of a device with a film-wire/substrate structure used in integrated circuits and flexible electronics. Acknowledgements The author Qinghua Wang acknowledges the financial support from the JSPS Postdoctoral Fellowship for Foreign Researchers.
Q. Wang et al. / Microelectronics Reliability 53 (2013) 652–657
The authors are grateful to the financial supported by the National Basic Research Program of China (‘‘973’’ Project) (Grant Nos. 2010CB631005, 2011CB606105), the National Natural Science Foundation of China (Grant Nos. 90916010, 11172151, 11232008) and Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20090002110048).
References [1] Hamers RJ. Flexible electronic futures. Nature 2001;412:489–90. [2] Wong WS, Salleo A. Flexible electronics: materials and applications. Springer Verlag; 2009. [3] Davis JA, Venkatesan R, Kaloyeros A, Beylansky M, Souri SJ, Banerjee K, et al. Interconnect limits on gigascale integration (GSI) in the 21st century. Proc IEEE 2001;89:305–24. [4] Pan B, Qian K, Xie H, Asundi A. Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review. Meas Sci Technol 2009;20:062001. [5] Peters W, Ranson W. Digital imaging techniques in experimental stress analysis. Opt Eng 1982;21. [6] Weller R, Shepard B. Displacement measurement by mechanical interferometry. Proc Soc Exp Stress Anal 1948;6:35–8. [7] Kishimoto S, Egashira M, Shinya N. Microcreep deformation measurements by a moire method using electron-beam lithography and electron-beam scan. Opt Eng 1993;32:522–6. [8] Takeda M, Suzuki J. Crystallographic heterodyne phase detection for highly sensitive lattice-distortion measurements. J Opt Soc Am A 1996;13:1495–500. [9] Liu Z, Xie H, Gu C, Meng Y. The digital geometric phase technique applied to the deformation evaluation of MEMS devices. J Micromech Microeng 2009;19:015012.
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[10] Wang QH, Xie HM, Hu ZX, Zhang J, Sun J, Liu G. Residual thermo-creep deformation of copper interconnects by phase-shifting SEM moiré method. Appl Mech Mater 2011;83:185–90. [11] Ling S, Fulong D. Application of refractive medium in optical micromechanics. Acta Mech Sinica 1994;10:360–6. [12] Xie H, Kishimoto S, Shinya N. Fabrication of high-frequency electron beam moire grating using multi-deposited layer techniques. Opt Laser Technol 2000;32:361–7. [13] Chou SY, Krauss PR, Renstrom PJ. Imprint lithography with 25-nanometer resolution. Science 1996;272:85–7. [14] Xie HM, Liu ZW, Zhang M, Chen PW, Huang FL, Zhang QM. Nano-grating fabrication technique. Key Eng Mater 2006;326:131–4. [15] Du H, Xie H, Guo Z, Pan B, Luo Q, Gu C, et al. Large-deformation analysis in microscopic area using micro-moire methods with a focused ion beam milling grating. Opt Lasers Eng 2007;45:1157–69. [16] Xie H, Kishimoto S, Li Y, Liu Q, Zhao Y. Fabrication of micro-moire gratings on a strain sensor structure for deformation analysis with micro-moire technique. Microelectron Reliab 2009;49:727–33. [17] Li Y, Xie H, Guo B, Luo Q, Gu C, Xu M. Fabrication of high-frequency moire gratings for microscopic deformation measurement using focused ion beam milling. J Micromech Microeng 2010;20:055037. [18] Hÿtch MJ, Putaux JL, Pénisson JM. Measurement of the displacement field of dislocations to 0.03 Å by electron microscopy. Nature 2003;423:270–3. [19] Hÿtch M, Snoeck E, Kilaas R. Quantitative measurement of displacement and strain fields from HREM micrographs. Ultramicroscopy 1998;74:131–46. [20] Wang Q, Xie H, Liu Z, Lou X, Wang J, Xu K, et al. Residual stress assessment of interconnects by slot milling with FIB and geometric phase analysis. Opt Lasers Eng 2010. [21] Lou XH. Principle and application of geometric phase method. Master thesis. Beijing Institute of Technology; 2009 [in Chinese]. [22] L.i.C. The Liduo alloy material Co., Solving complex chemical equilibria using a geometric-programming based technique [20100911]. .
Contents lists available at SciVerse ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel
In situ high temperature creep deformation of micro-structure with metal film wire on flexible membrane using geometric phase analysis Qinghua Wang a,b, Satoshi Kishimoto a, Huimin Xie b,⇑, Zhanwei Liu c, Xinhao Lou c a
National Institute for Materials Science, Tsukuba, 305-0047 Ibaraki, Japan AML, Department of Engineering Mechanics, Tsinghua University, 100084 Beijing, China c School of Aerospace Engineering, Beijing Institute of Technology, 100081 Beijing, China b
a r t i c l e
i n f o
Article history: Received 8 July 2012 Received in revised form 5 October 2012 Accepted 23 October 2012 Available online 8 December 2012
a b s t r a c t A way of measuring the in situ high temperature creep deformation of a micro-structure with a metal film wire on a flexible membrane is developed. The creep deformation measurement of a micro-structure with a Karma alloy wire on a polyimide membrane is used as an application. High temperature gratings were fabricated directly on the surfaces of two Karma alloy wires using the focused ion beam milling technique after the grating frequencies were designed. The grating morphologies with different isothermal soaking time were recorded by a scanning electron microscope with a heating apparatus. The in situ high temperature creep deformations in a micro-region of the structure were measured by performing the geometric phase analysis. The creep behaviors of this structure at 300 °C and 500 °C were analyzed. The developed measurement method is prospective in evaluating the reliability of the film-wire/substrate structures at a high temperature. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The structures composed of metal film wires and flexible substrates have been extensively adopted in the semiconductor integrated circuits, micro–electro-mechanical systems, and flexible electronic devices [1,2]. With the development of miniaturization and integration, the characteristic dimension of metal film wires has reached the micron and submicron levels [3]. During the application process, the film-wire/substrate structures are usually employed in high temperature environments. The stability of a structure at a high temperature is closely related to its creep behavior. However, the complexity of a film-wire/substrate structure makes it very difficult to investigate the high temperature deformation of the structure. To our knowledge, few reports study the deformation of a micro-structure with a metal film wire on a flexible substrate at a high temperature. In this study, we attempt to develop a measurement method to explore the in situ high temperature creep deformation of a micro-film-wire/substrate structure, and a structure with a Karma alloy wire on a polyimide membrane is used to illustrate this method. A speckle pattern and a grating pattern are two basic deformation carriers in optical methods. In general, the surface topography of a deformation carrier on a metal film wire at the micrometer scale is observed using a high power microscope. A speckle pattern
⇑ Corresponding author. E-mail address: [email protected] (H. Xie). 0026-2714/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.microrel.2012.10.016
is often used in the digital image correlation (DIC) method [4,5]. However, the brightness and the contrast of a speckle pattern need to be frequently adjusted at a high temperature in a scanning electron microscope (SEM), which limits the application of the DIC method on the high temperature deformation measurement of a micro-structure. A grating pattern is a basic component in moiré methods [6,7] and the geometric phase analysis (GPA) technique [8,9], which are not affected by the brightness and the contrast of the grating pattern in a SEM. As a consequence, a high temperature grating becomes a good choice to analyze the high temperature creep deformation of a micro-structure [10]. Common micro-grating fabrication techniques include photolithography, electron beam lithography, nanoimprint lithography, atomic force microscope ruling and focused ion beam (FIB) milling. Photolithography such as the holographic interferometry lithography technique is able to generate gratings with frequencies up to several thousands of lines per millimeter [11]. Electron beam lithography is reported to be capable of fabricating a 10,000 lines/mm grating on a silicon wafer [12]. Nanoimprint lithography provides an easy way to produce micro- and nano-gratings [13]. However, photoresists are necessary in the above three techniques, and high-temperature photoresists are very expensive. The atomic force microscope ruling method can be utilized to fabricate a grating with a frequency of tens of thousands of lines per millimeter [14]. Nevertheless, the concave–convex structure with a film wire on a substrate is likely to damage an atomic force microscope probe. The FIB milling technique without the need for photoresist is known as a powerful micro-machining tool, having many advantages such
Q. Wang et al. / Microelectronics Reliability 53 (2013) 652–657
653
as high resolution, convenient location and high milling speed [15–17]. Based on the FIB milling technique, high temperature micro-gratings can be fabricated on the surface of a Karma alloy wire on a polyimide membrane. To investigate the in situ creep deformation of a microfilm-wire/substrate structure, a SEM with a heating apparatus is used both for heating and observation in this study. Because the movement of the sample stage of the SEM with a heating apparatus cannot be quantitatively controlled, it is hard to apply the phase shifting SEM moiré method which can improve the measurement accuracy of the SEM moiré method. Fortunately, the GPA technique with a high measurement accuracy [18], which can directly analyze the grating images, provides a feasible way to determine the sample deformation in a SEM with a heating apparatus. After the grating frequencies are designed according to the structure size and the SEM condition, the creep deformations of the structure with a Karma alloy on a polymer membrane are investigated in this study. Fig. 1. Sample morphology and the sketch map of the structure.
2. Principle of geometric phase analysis GPA is able to obtain the deformation information from calculating the local Fourier components of lattice fringes [18]. If an image includes a grating with a frequency of f ðrÞ and the displacement is uðrÞ after deformation, the displacement is directly related to the phase difference DP f ðrÞ of the image [18,19]:
uðrÞ ¼
DPf ðrÞ 2pf ðrÞ
ð1Þ
The strain can be obtained from the first derivative of the displacement. For instance, if there are two frequencies (f1 and f 2 ) in an image, the displacement and the strain components can be expressed by:
ux uy
¼
exx exy eyx eyy
1 2p
¼
f1x
f1y
f2x
f2y
1 2p
1
P f1
ð2Þ
P f2
f1x
f1y
f2x
f2y
1
@Pf1 =@x @Pf1 =@y @Pf2 =@x @Pf2 =@y
ð3Þ
where ux ; uy indicate the displacement components in the X, Y directions, respectively, exx ; eyy ; exy express the strain components in the X, Y directions as well as the shearing strain, respectively, f1x ; f1y ; f2x ; f2y are the frequency components in the X, Y directions, respectively, and Pf 1 ; Pf 2 represent the phases corresponding to f1 ; f2 , respectively [20]. As long as the grating images before and after deformation are recorded, the displacement and the corresponding strain will be able to be obtained from the GPA technique. 3. Experimental details 3.1. Sample preparation The sample consists of a Karma alloy wire and a polyimide (PI) membrane, which is fabricated by photolithography. The Karma alloy wire is distributed in a sequential narrow ‘S’ shape. The Karma alloy contains 73% nickel, 20% chromium, and a small quantity of aluminum, iron and manganese. Due to excellent performances, the Karma alloy is widely used as a main component of a resistance strain gauge working in high temperature or low temperature environments. The PI membrane commonly serves as a flexible substrate, which has extensive applications in flexible electronic devices such as flexible screens, electronic papers and artificial skins.
The morphology and the structure of the sample are illustrated in Fig. 1. The thickness, the width and the length of the Karma alloy wire are 4 lm, 66 lm and 10 mm, respectively. The spacing between two adjacent segments of the Karma alloy wire is 134 lm. The thickness, the width and the length of the whole PI membrane are 30 lm, 6 mm and 16 mm, respectively. 3.2. Micro-grating design and fabrication To perform the GPA, a grating is necessary to be fabricated on the surface of the Karma alloy wire. If the grating frequency is too low, the accuracy of deformation measurement will not meet the requirement. On the other hand, if the grating frequency is too high, the grating region will be very small, the FIB milling time will be very long and the grating quality will be poor due to the unsmooth surface of the Karma alloy wire. Even if a grating with a little better quality could be fabricated, it is very hard to obtain a clear grating image, because the magnification of a SEM with a heating apparatus is limited within 2000. The higher the temperature is, the harder the SEM imaging becomes, and only the image of a lower-frequency grating can be clear when the temperature reaches 500 °C. We have carried out some experiments and found that it is appropriate when the grating frequency is in the range of 1000–2500 lines/mm. Two cross gratings with frequencies of 2000 lines/mm and 1000 lines/mm are chosen to be fabricated on the Karma alloy wire surfaces of two samples, respectively. Sample 1# with the 2000 lines/mm grating is used to investigate the creep behavior of the sample in a micro-region at 300 °C, and sample 2# with the 1000 lines/mm grating is aimed at the creep behavior at 500 °C. The sample stage is tilted at 50°, the accelerating voltage of the ion beam is set to be 30 kV and the free working distance is 18 mm when the two gratings are fabricated in a FIB system. The axial direction of the Karma alloy wire should be adjusted to be parallel or perpendicular to the horizontal direction before grating fabrication. As a result, the two principle directions of the cross grating will be parallel and perpendicular to the axis direction of the Karma alloy wire, respectively. The choice of a cross grating over a one-way grating is to eliminate the calculation error when the principle direction of the one-way grating is not exactly parallel to the wire axial direction. The SEM images of the cross grating with a frequency of 2000 lines/mm on sample 1# are displayed in Fig. 2. The enlarged view (Fig. 2a) and the global view (Fig. 2b) of the grating show the grating topography and the location of the grating region,
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(a) enlarged view
(b) global view
Fig. 2. SEM images of the cross grating with a frequency of 2000 lines/mm fabricated by FIB on the surface of the Karma alloy wire of sample 1#.
respectively. The depth of the grating is 0.2 lm, less than one-tenth of the thickness of the Karma alloy wire (4 lm). Therefore, the effect of the grating on the Karma alloy wire is negligible. The width and the length of the grating region are 50 lm and 100 lm, respectively. Only a part of the grating region is observed during the heating process in a SEM. The SEM images of the 1000 lines/mm grating on sample 2# are shown in Fig. 3. Because this grating will be used at 500 °C, the grating depth must be larger enough to ensure clear grating images recorded by a SEM. The grating depth is set to be 0.4 lm, one-tenth of the thickness of the Karma alloy wire. The width and the length of the grating region are 26 lm and 80 lm, respectively, where the width is less than half of the wire width. Consequently, the influence of the 1000 lines/mm grating on the Karma alloy wire can also be ignored. 3.3. High temperature creep experiments A Shimadzu SEM with a heating apparatus is utilized to carry out the experiments of heating, isothermal soaking and observation of the samples (Fig. 4a). To avoid the crimping of the PI membrane at a high temperature, the sample with the Karma alloy wire on the polyimide membrane should be fixed on a rigid substrate.
(a) enlarged view
According to the shape and the dimensions of the standard tensile specimen of this SEM, a dumbbell sample base made from SUS304 stainless steel (SS) is fabricated, as seen in Fig. 4b. The thickness of the SS base is 1 mm. After the marginal regions of a sample made up of the Karma alloy wire and the PI membrane are cut, the two ends of the sample are pasted on the surface of the SS base by high temperature glue. It should be noted that the grating region on the sample should be placed in the central region along the length of the SS base. So that the grating images can be recorded from the observation window of the SEM during the heating and the isothermal soaking processes. A pre-tensile load of 0.03 kN is exerted on the SS base in the SEM before heating. To avoid the shift of the SS base, the preload is kept unchanged during the processes of heating and isothermal soaking. The heating rate of the heating apparatus in the SEM is set to be 20 °C/min. Before the grating images are recorded, we should make sure that the axis of the Karma alloy wire is parallel to the vertical or the horizontal direction and the grating images fill the entire screen. Sample 1# with the 2000 lines/mm grating is kept at 300 °C for 240 min to study its micro-region creep behavior. The grating images are recorded every 60 min at the beginning, and every 30 min two hours later. Sample 2# with the 1000 lines/mm grating
(b) global view
Fig. 3. SEM images of the cross grating with a frequency of 1000 lines/mm fabricated by FIB on the surface of the Karma alloy wire of sample 2#.
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duced by the creep deformation are displayed in Fig. 5b and c, respectively. The strain distribution is calculated by Eq. (3), and the average strain along the wire axis is e = 0.0226. Using the same calculation process, the micro-region creep deformations of the samples at 300 °C and 500 °C at different isothermal soaking time are acquired by GPA. The relationships between the micro-region creep strain and the isothermal soaking time of the samples at 300 °C and 500 °C are plotted in Figs. 6 and 7, respectively. All the micro-region creep strains are compressive, and the absolute value of strain increases with the increasing isothermal soaking time. The maximal absolute value of the microregion creep strain at 300 °C is 0.0171, and the maximal value reaches 0.0347 at 500 °C.
Electron beam
Grating Karma alloy
PI SUS304
4.2. Discussion
Heating apparatus in SEM
(a) Experimental setup
SUS304
(b) Size of a standard tensile specimen with a thickness of 1mm (Unit: mm) Fig. 4. Schematic diagram of the experimental setup and the standard tensile specimen under a Shimadzu SEM with a heating apparatus, in which the red line expresses the high temperature glue and the pink rectangle stands for the sample. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
is kept at 500 °C for 300 min, and the grating images are collected at intervals of 60 min. 4. Results and discussion 4.1. Creep deformation measurement The grating images at 300 °C and 500 °C before the isothermal soaking process (zero time) are treated as the reference grating images. The distributions of the phase differences and the displacements of the grating images at different isothermal soaking time can be calculated by GPA. The corresponding strain fields will then be obtained from the partial derivatives of the displacement fields. The average value of a strain field is just the micro-region strain at this moment. When the strain ranges from 1 105 to 1 101, the calculated strain error is less than 5% [21]. The creep deformation of the structure with the Karma alloy wire on the PI membrane along the wire axis is mainly concerned. Taking sample 2# at 500 °C for 60 min as an example, the calculation process of GPA for the deformation will be presented. The 1000 lines/mm grating at 500 °C before the isothermal soaking process is considered as the reference image. Fig. 5a shows the calculation area on the sample surface. The distributions of the phase difference and the displacement of sample 2# at this moment in-
During the processes of heating and isothermal soaking, four layers of the structure, i.e., the Karma alloy wire, the PI membrane, the high temperature glue and the SUS304 SS base, interact with each other. The corresponding material constants are listed in Table 1. It is clear that the thickness of the SS base is much greater than those of the other three layers, and (EA)SS (EA)karma, (EA)SS (EA)PI, (EA)SS (EA)glue, where E, A represent the Young’s modulus and the cross sectional area respectively. Consequently, we can suppose that the SS base is free to undergo thermal expansion as if the other three layers do not exist. The locations of the Karma alloy wire, the PI membrane and the high temperature glue are determined by the SS base. In consideration of the slender characteristics, it is assumed that the Karma alloy wire, the PI membrane and the SS base experience linear expansion only along the length direction. When the environmental temperature in the SEM rises from the room temperature to a high temperature, a pre-tensile stress will exist in the Karma alloy wire because the thermal expansion coefficient (TEC) of the Karma alloy is smaller than that of SS, and a pre-compressive stress will exist in the PI membrane as the TEC of PI is greater than that of SS. The effect of the small pre-tensile load of the SS base on the deformation of the composite structure is ignored in the above analysis. The two parts of the high temperature glue will expand along their length directions which are perpendicular to the axial direction of the SS base, as seen from Fig. 4b. Due to the greater TEC of the high temperature glue compared with the SS base, there will be pre-compressive stress in the glue. However, the pre-compressive stresses and the creep deformations of the two parts of the glue will not affect the deformation of the composite structure of the Karma alloy wire and the PI membrane, because the length directions of the glue parts are perpendicular to the length direction of the composite structure. As we all know, the creep temperature of a polymer material is higher than its glass transition temperature (GTT), and the creep temperature of a metal is greater than 0.3–0.4Tm, where Tm is the thermodynamic melting point. According to the data in Table 1, the creep temperatures of the PI membrane, the Karma alloy wire and the SS base are 280 °C, 214–376 °C, 232– 400 °C respectively. At 300 °C, the PI membrane has begun to creep, but the Karma alloy wire and the SUS304 SS base have not yet entered or are just beginning to enter the creep range. Due to the pre-compressive stress in the PI membrane, a compressive deformation occurs in the micro-region in the PI membrane during the creep process. The Karma alloy wire on the PI membrane will also get a compressive deformation. This is the reason why the micro-region creep strain in Fig. 6 is negative. The creep deformation of the high temperature glue in the width direction of the SS base and the unchanged preload of the SS base during the isothermal soaking
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(a) calculation area
(c) displacement (0.076 m/pixel)
(b) unwrapped phase
Fig. 5. Micro-region creep deformation of the structure with the Karma alloy wire on the PI membrane at 500 °C for 60 min.
Table 1 Material constants of the Karma alloy wire, the PI membrane, the high temperature glue and the SUS304 SS base, where GTT is glass transition temperature and TEC is thermal expansion coefficient.
Fig. 6. Variation of the micro-region creep strain of the structure with the Karma alloy wire on the PI membrane along with the isothermal soaking time at 300 °C.
Material
Young’s modulus E (GPa)
Thickness h (lm)
TEC a (106 K)
GTT or melting point (°C)
PI Glue Karma alloy SS
2.0 3.6 210
30 33 4
30 80–110 11.8
193
1000
17.3
280 (GTT) – 1350 (melting) [22] 1410 (melting)
At 500 °C, all the four materials have entered the creep stage. The absolute value of the micro-region creep deformation of the PI membrane (polymer) is greater than that of the Karma alloy wire and the SUS304 SS base (metals). Finally, a compressive deformation appears in the micro-region of the structure with the Karma alloy wire on the PI membrane owing to the compatibility of deformation (Fig. 7). 5. Conclusion
Fig. 7. Variation of the micro-region creep strain of the structure with the Karma alloy wire on the PI membrane along with the isothermal soaking time at 500 °C.
process will not influence the creep deformation of the composite structure. The absolute values of the micro-region creep strain along with the isothermal soaking time in Fig. 6 indicate that the PI membrane has a poor resistance to the creep deformation at 300 °C. It is generally thought that the PI membrane can work for a long term in the environment of 260 to 300 °C. However, greater micro-region creep strain of the PI membrane will arise at 300 °C under long isothermal soaking time from this study. It suggests that the PI membrane is not suitable for a long-term use for micro-analysis at 300 °C.
In this study, an approach based on the FIB milling technique and geometric phase analysis is developed to study the in situ high temperature creep behavior of a micro-structure with a metal film wire on a flexible membrane. The in situ high temperature creep deformation of the micro-structure with a Karma alloy wire on a polyimide membrane is investigated. Two high temperature cross gratings are designed and successfully fabricated on two samples. Gratings with frequencies of 2000 lines/ mm and 1000 lines/mm are used at 300 °C and 500 °C in a SEM with a heating apparatus, respectively. The in situ high temperature creep deformations in micro-regions of the samples are measured and analyzed taking advantage of geometric phase analysis. This work provides a simple and effective way to investigate the in situ high temperature creep behaviors of the filmwire/substrate structures. The approach described in this study has a good potential to assess the stability of a device with a film-wire/substrate structure used in integrated circuits and flexible electronics. Acknowledgements The author Qinghua Wang acknowledges the financial support from the JSPS Postdoctoral Fellowship for Foreign Researchers.
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The authors are grateful to the financial supported by the National Basic Research Program of China (‘‘973’’ Project) (Grant Nos. 2010CB631005, 2011CB606105), the National Natural Science Foundation of China (Grant Nos. 90916010, 11172151, 11232008) and Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20090002110048).
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