- Email: [email protected]
NEMS applications using nanoindentation techniques
Surface and Coatings Technology 163 – 164 (2003) 521–526
Fatigue studies of nanoscale structures for MEMSyNEMS applications using nanoindentation techniques Xiaodong Li, Bharat Bhushan* Nanotribology Laboratory for Information Storage and MEMSyNEMS, Department of Mechanical Engineering, The Ohio State University, 206 West 18th Avenue, Columbus, OH 43210-1107, USA
Abstract Mechanical properties of nanoscale structures are needed to design reliable microynanoelectromechanical systems (MEMSy NEMS). Most material properties are known to be size-dependent and such properties of the nanoscale structures have not been well characterized. Bending strength and fatigue properties of nanoscale silicon beams with a 6-mm length, a 255 nm height and widths ranging from 400 to 800 nm were evaluated using a depth-sensing nanoindenter with a harmonic force. In the bending tests, the beams failed in a brittle manner with a flat fracture surface. Load cycles used in continuous stiffness measurement were used to perform fatigue tests. The contact stiffness was monitored continuously throughout the fatigue test. The abrupt decrease in the contact stiffness indicates fatigue damage has occurred. Cleavage steps were found on the fatigue fracture surface. Failure mechanisms of the beams during bending and fatigue are also discussed in conjunction with the surface to volume ratio, surface defects, and cleavage planes. The dynamic nanoindentation fatigue test used in this study can be satisfactorily used to evaluate the fatigue behavior of nanoscale structures for use in MEMSyNEMS. 䊚 2002 Elsevier Science B.V. All rights reserved. Keywords: Nanoindentation; Continuous stiffness measurement; Silicon; Bending strength; Fatigue
1. Introduction Recent developments in science and engineering have advanced capability to fabricate and control structures on the scale of nanometers, and have brought problems of material behavior on the nanometer scale into the domain of engineering. Reliability studies are the key for practical application and commercialization of today’s advanced microynanoelectromechanical systems (MEMSyNEMS). Many current and potential applications for MEMSyNEMS are not really practical, because their mechanical properties have not been established, and are, to a large extent, still unknown w1–3x. Mechanical and structural aspects are of critical importance in determining long-term stability of such small structures. Precise characterization of the mechanical properties at the nanoscale is required for proper design and structureminiaturization. Recent studies have revealed that material properties are size-dependent w2,4x. However, current *Corresponding author. Tel.: q1-614-292-0651; fax: q1-614-2920325. E-mail address: [email protected] (B. Bhushan).
software developed for designing microynanoscale devices is based on bulk material properties without considering the size-dependent phenomenon. This limits the further development and application of MEMSy NEMS. Single-crystal silicon and silicon-based materials are the most common materials used in MEMSyNEMS. An early study showed silicon to be a mechanically resilient material in addition to its favorable electronic properties w5x. However, recent studies show that silicon is not good in friction and wear because of its poor fatigue properties w2,3x. Characterization of the fatigue properties is vital to designing MEMSyNEMS because moving components involved in these devices are subjected to cyclic loading. The current understanding of material fatigue is, to a large extent, based on metals. Fatigue of metals is associated with the generation and motion of dislocations and accumulation of plastic deformation. Single-crystal silicon has very limited dislocation mobility at room temperature, making the possibility of cyclic fatigue failure far less obvious w6x. It is generally accepted that in brittle materials, fatigue can only take
0257-8972/03/$ - see front matter 䊚 2002 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 7 - 8 9 7 2 Ž 0 2 . 0 0 6 6 2 - X
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place in toughened solids. However, recent studies show that single-crystal silicon thin films can degrade and fail under cyclic loading conditions in ambient air at room temperature w6,7x. Crack-growth can occur under cyclic loading conditions. Studies on fatigue of nanoscale-sized silicon structures are lacking w8x. Cyclic fatigue failure in silicon has not been well studied, especially at the nanoscale. It is uncertain if traditional fatigue theory is applicable to such small structures. A recently developed technique, continuous stiffness measurement (CSM) w9,10x, offers a significant improvement in nanoindentation testing. Load cycles used in the CSM can be used to perform fatigue tests at the nanoscale w11,12x. This paper presents an attempt to measure bending strength and fatigue properties of fixed nanoscale silicon beams. Scanning electron microscope (SEM) observations of the bending and fatigue fracture surfaces are also presented to help understand the deformation modes of the beam materials under bending and fatigue. 2. Experimental procedure 2.1. Fabrication of nanometer-scale specimens Single-crystal silicon fixed nanobeams were fabricated by bulk micromachining incorporating enhancedfield anodization using an AFM (Seiko Instruments Inc., SPA-300HV) on a (0 0 1) plane of an Si wafer separated by implanted oxygen (SIMOX) w13x. The trench (width of 6 mm) is first etched from the underside after which the top silicon dioxide (SiO2) layer is etched to expose the Si diaphragm. A line of SiO2 film with a width of less than 1-mm is deposited by field-enhanced anodization on the Si surface. This SiO2 film was used as a high-precision mask pattern for anisotropic wet etching with a solution of 20% tetra-methyl ammonium hydroxide (TMAH). It was then possible to fabricate a nanometer-scale Si structure after etching. The line pattern of SiO2 film was drawn by applying a bias voltage between an Au-coated cantileverytip and the Si diaphragm in air at room temperature. In this study, a bias voltage of 20 V and a cantilever speed of 0.4 mmys were selected, which resulted in smooth film lines as well as a film thickness higher than the 4 nm required for reliable TMAH wet etching of the Si interface on the (0 0 1) plane w13x. The Si diaphragm had an average thickness of 255 nm and hence this is the average thickness of the Si beams. Fig. 1 shows the SEM image of the Si nanobeams and a schematic of a typical nanobeam. The Si beams are oriented along the w1 1 0x direction in the (0 0 1) plane. The cross-section of the beams is trapezoidal owing to the anisotropic wet etching process. The crosssection for the beams exhibits a small amount of curvature as compared to the relatively well-defined trapezoidal shape of the Si beams due to the oxidation
Fig. 1. (a) SEM micrograph of nanobeam specimens and (b) a schematic of the shape of a typical nanobeam. The trapezoidal cross-section is due to the anisotropic wet etching during the fabrication.
process. The actual width, length and thickness values of the beams were measured using a SEM. Surface roughness measurements of the beam surfaces in tapping mode yielded a s of 0.7"0.2 nm and peak-to-valley (P–V) distance of 4"1.2 nm for Si. Prior to testing, the silicon samples were cleaned by immersing them in a ‘piranha etch’ solution (3:1 solution by volume of 98% sulphuric acid and 30% hydrogen peroxide) for 10 min to remove any organic contaminants. 2.2. Bending and fatigue tests Bending and fatigue experiments were carried out using a Nano Indenter II䉸 (MTS Systems Corp.) equipped with the CSM option. This instrument monitors and records the dynamic load and displacement of the indenter during indentation with a force resolution of approximately 75 nN and displacement resolution of approximately 0.1 nm. To avoid the indenter tip pushing into the specimen, a blunt tip should be used in the bending and fatigue tests. In this study, a diamond conical indenter with a radius of 1 mm and an included angle of 608 was used. Loading position was at the center of the span. An optical microscope with a magnification of 1500= was used to locate the center of the span. Then the specimen was moved by using a lead screw under the indenter location with a resolution
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of approximately 200 nm in longitudinal direction and less than 100 nm in lateral direction. Fig. 2 shows the schematic of bending and fatigue tests on a nanoscale Si beam using a depth-sensing nanoindenter with a harmonic force. The load is applied at the center of the span. In a rectangular beam, the maximum moments occur under the load and at the fixed ends. Due to the trapezoidal cross-section, the maximum moment (tensile bending stresses) occurs at the top surfaces at fixed ends. The CSM technique has been described in detail in Refs. w9,10x. Briefly, a harmonic force is added to the nominally increasing load, P, on the indenter. The displacement response of the indenter at the excitation frequency and the phase angle between the two are measured continuously as a function of depth. Solving for the in-phase and out-ofphase portions of the response results in an explicit determination of the contact stiffness as a continuous function of depth. The CSM technique provides load cycles of a sinusoidal shape at high frequencies that can be used to perform fatigue tests. The fatigue behavior of coatings can be studied by monitoring the change in contact stiffness since the contact stiffness is sensitive to the damage formation. To obtain deformation and damage during fatigue loading, large amplitude oscillations were used. The numbers of cycles were determined from the elapsed time. Load cycles are applied to the coating, resulting in a cyclic stress; P is the cyclic load, Pmean is the mean load, Pos is the oscillation load amplitude, and v is the oscillation frequency. All fatigue tests were conducted at an excitation frequency of 45 Hz. 3. Results and discussion 3.1. Elastic modulus and bending strength Fig. 3a shows the load–displacement curve for the Si beam that was bent to failure. The length, upper and lower widths of the beam used in the bending test are 6 mm, 400 and 800 nm, respectively. The beam showed linear behavior followed by abrupt failure. The nonlinear behavior at higher loads may result from the high surface to volume ratio of the beam. This will be discussed later. Elastic modulus and bending strength (fracture stress) of the beams can be estimated by equations based on the assumption that the beams follow linear elastic theory of an isotropic material. For a fixed elastic beam loaded at the center of the span, the elastic modulus is expressed as Es
l3 m 192I
(1)
where l is the beam length, I is the area moment of inertia for the beam cross-section and m is the slope of the load–displacement curve during bending w14x. The
Fig. 2. (a) A schematic of the bending moments generated in the beam during a bending experiment, with the load at the center of the span. (b) A schematic of the fatigue moments generated in the beam during a fatigue experiment.
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Fig. 3. (a) Load–displacement curve of a Si nanobeam (400 nm upper width, 800 nm lower width and 6 mm length) obtained from a nanoindentation experiment. (b) SEM image of the fracture surface of the beam broken during bending. (c) Bending stress distribution obtained from finite element modeling, showing that the maximum tensile stresses occur on the top surfaces near the fixed ends.
area moment of inertia is calculated from the following equation: Is
w21q4w1w2qw22 3 t, 36Žw1qw2.
(2)
where w1 and w2 are the upper and lower widths, respectively, and t is the thickness of the beam. According to linear elastic theory, for a centrally loaded beam, the moment diagram is shown in Fig. 2a. The maximum moments are generated at the ends (negative moment) and under the loading point (positive moment). Then bending stresses generated in the beam are proportional to the moments and are compressive or tensile about the neutral axis (line of zero stress). The maximum tensile stress (sb, which is the fracture stress) is produced on the top surface at both the ends and is given by w14x s bs
Fmaxle1 8I
(3)
where Fmax is the applied load at failure, l is the length of the beam and e1 is the distance of the top surface from the neutral plane of the beam cross-section and is given by w14x e 1s
tŽw1q2w2. 3Žw1qw2.
(4)
Although the moment value at the center of the beam is the same as at the ends, the tensile stresses at the center (generated on the bottom surface) are less than those generated at the ends (per Eq. (2)) because the distance from the neutral axis to the bottom surface is less than e1. This is because of the trapezoidal crosssection of the beam, which results in the neutral axis being closer to the bottom surface than the top (Fig. 2). Finite element model result shows that the maximum tensile bending stresses occurred near the ends as shown in Fig. 3c. The calculated elastic modulus and bending strength values are 187 and 17.5 GPa, respectively. Previously reported bulk elastic modulus of Si (1 1 0)
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is 169 GPa w15x and bending strength of microscale Si specimens is on the order of 6 GPa w6x. Difference in elastic modulus between the measured and reported values might result from the offset of loading from the beam center. Bending strength shows a clear specimen size dependence with nanoscale numbers being twice as large as numbers reported for larger scale specimens w6x. The offset of loading from the beam center cannot cause such high strength. High pressure can result in phase transformation in silicon. This phase transformation might contribute to the strength of the silicon beam. For the nanoscale specimens, the surface to volume ratio is much higher than for the micro- and macroscale specimens. Surface atoms can move more easily than the atoms locked in the lattice. This makes the nanoscale specimen more difficult to initiate cracks on its surface. This is probably why the nanoscale specimen has higher bending strength than the lager scale specimen. Fig. 3b shows the SEM image of the fracture surface of the beam broken during bending. The fracture surface is perpendicular to the beam length direction. The fracture surface is flat without any plastic deformation bands. This is a typical characteristic of brittle fracture. 3.2. Fatigue behavior Fig. 4a shows the contact stiffness as a function of the number of cycles for a nanoscale Si beam (upper widths380 nm, lower widths790 nm and lengths6 mm) cyclically deformed by an oscillation load amplitude of 25 mN with a mean load of 100 mN at a frequency of 45 Hz. A plateau is observed followed by an abrupt decrease in contact stiffness at 0.6=104 cycles. The abrupt decrease in contact stiffness indicates that fatigue damage has occurred, which can be used to determine fatigue life. This suggests that the failure of the beam occurs after progressive accumulation of damage, e.g. by the stable propagation of a crack. The above results show that premature fatigue occurred in nanoscale single-crystal silicon beams. The frequency used in the fatigue test (45 Hz) is much lower than the resonant frequency (55 MHz) of the beam. Therefore, the beam damage results from the cyclic loading of the indenter and not from the resonance of the beam itself. Silicon has been regarded as a brittle material. There has been no evidence of bulk silicon being susceptible to fatigue failure. This is probably because bulk tests cannot resolve the low crack-growth rates relevant to microynanoscale beams w6x. Recent studies show that micro-sized single-crystal silicon beams can degrade and fail under cyclic loading conditions in ambient air at room temperature w6,7x. In our study, the mean stress and stress amplitude are 9.8 and 2.4 GPa, respectively. The maximum stress (12.2 GPa) is 30% lower than the bending strength (fracture stress). The fatigue fracture
Fig. 4. (a) Contact stiffness as a function of the number of cycles for a Si nanobeam (380 nm upper width, 790 nm lower width and 6 mm length) cyclically deformed by an oscillation load amplitude of 25 mN with a mean load of 100 mN at a frequency of 45 Hz. (b) SEM image of the fracture surface of the beam broken during fatigue, indicating cleavage steps.
surface is rough with steps, as shown in Fig. 4b. This indicates that initiation and propagation of the fatigue cracks oriented during failure. However, it is difficult to correlate the growth of cracks from the fracture surface. The steps at the fatigue fracture surface result from the transition in crack path manifesting itself in terms of dissipating energy w6x. Flaws on the beam surface can be fatigue sources w6,7x. Native oxide (SiO2) layer forms on the Si beam surface upon reaction with the atmosphere. More SiO2 can form at the flaws where surface stress is relatively higher than other places. SiO2 has much lower bending strength (7.6 GPa) and fracture toughness (0.6 MPa m1y2) than single-crystal silicon (bending strengths17 GPa; fracture toughnesss 1.7 MPa m1y2) w8x. During the fatigue test, cracks can initiate in the SiO2 layer at the flaw sites. At room temperature, dislocation activity is very low in singlecrystal silicon. The dominant failure mode is cleavage. The morphology of the step-like surface is a direct result of the crystallography of cleavage. It is well known that the {1 1 1} planes are cleavage planes for single-crystal silicon. Cleavage steps form on {1 1 1} fracture surfaces as a means of dissipating energy during failure w6x. These cracks tend to propagate by cracking along multiple {1 1 1} cleavage planes to form steps. It has
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been reported that high pressure can cause phase transformation in single-crystal silicon. The phase transformation can induce localized stressystrain, which may assist cracks in initiation and propagation. This study clearly demonstrates that fatigue properties of nanoscale specimens can be studied by using the CSM technique.
this research was provided by the National Science Foundation (Contract No. ECS-9820022). The content of this information does not necessarily reflect the position or policy of the Government and no official endorsement should be inferred. References
4. Conclusions A technique to perform bending and fatigue tests of nanometer scale fixed beam specimens made of singlecrystal silicon using a depth-sensing nanoindenter with a harmonic force has been described. The nanoscale beams exhibited higher bending strength than the larger scale specimens. Load cycles used in the CSM were used to study the fatigue properties of nanoscale Si beams. Fatigue behavior of the beams was monitored by a change in the contact stiffness. Cleavage steps were found on the fatigue fracture surface. The nanoindentation bending and fatigue tests used in this study can be satisfactorily used to evaluate the bending strength and fatigue properties of nanoscale structures for use in MEMSyNEMS. Acknowledgments The nanobeam samples were prepared by T. Namazu and Prof. Y. Isono of the Department of Mechanical Engineering at Ritsumeikan University, Japan. The authors would like to thank Nano Innovation Center, MTS Corporation, TN for technical support and Dr S. Sundararajan for engaging in several useful discussions during the course of this study. Financial support for
w1x B. Bhushan (Ed.), Tribology Issues and Opportunities in MEMS, Kluwer Academic Publishers, Dordrecht, Netherlands, 1998. w2x B. Bhushan, Handbook of MicroyNanotribology, second ed., CRC, Boca Raton, FL, 1999. w3x B. Bhushan, Modern Tribology Handbook, vol. 1—Principles of Tribology; vol. 2—Materials, Coatings, and Industrial Applications, CRC Press, Boca Raton, FL, 2001. w4x B. Bhushan, A.V. Kulkarni, W. Bonin, J.T. Wyrobek, Phil. Mag. A 74 (1996) 1117–1128. w5x K.E. Petersen, Proc. IEEE 70 (1982) 420. w6x C.L. Muhlstein, S.B. Brown, R.O. Ritche, J. Microelectromech. Syst. 10 (2001) 593–600. w7x T. Ando, M. Shikida, K. Sato, Sensors and Actuators A 93 (2000) 70–75. w8x S. Sundararajan, B. Bhushan, Sensors and Actuators 48 (2002) 11–36. w9x J.B. Pethica, W.C. Oliver, Thin films: stresses and mechanical properties, in: J.C. Bravman, W.D. Nix, D.M. Barnett, D.A. Smith, (Eds.), Mat. Res. Soc., Pittsburgh, 130 (1989) 13–23. w10x W.C. Oliver, G.M. Pharr, J. Mater. Res. 7 (1992) 1564–1583. w11x X. Li, B. Bhushan, Mater. Charact., 48 (2002) 11–36. w12x X. Li, B. Bhushan, J. Appl. Phys. 91 (2002) 8334–8336. w13x T. Namazu, Y. Isono, T. Tanaka, J. Microelectromech. Syst. 9 (2000) 450–459. w14x R.J. Roark, Formulas for Stress and Strain, McGraw-Hill, New York, 1965. w15x B. Bhushan, S. Venkatesan, Adv. Info. Storage Syst. 5 (1993) 211–239.
Fatigue studies of nanoscale structures for MEMSyNEMS applications using nanoindentation techniques Xiaodong Li, Bharat Bhushan* Nanotribology Laboratory for Information Storage and MEMSyNEMS, Department of Mechanical Engineering, The Ohio State University, 206 West 18th Avenue, Columbus, OH 43210-1107, USA
Abstract Mechanical properties of nanoscale structures are needed to design reliable microynanoelectromechanical systems (MEMSy NEMS). Most material properties are known to be size-dependent and such properties of the nanoscale structures have not been well characterized. Bending strength and fatigue properties of nanoscale silicon beams with a 6-mm length, a 255 nm height and widths ranging from 400 to 800 nm were evaluated using a depth-sensing nanoindenter with a harmonic force. In the bending tests, the beams failed in a brittle manner with a flat fracture surface. Load cycles used in continuous stiffness measurement were used to perform fatigue tests. The contact stiffness was monitored continuously throughout the fatigue test. The abrupt decrease in the contact stiffness indicates fatigue damage has occurred. Cleavage steps were found on the fatigue fracture surface. Failure mechanisms of the beams during bending and fatigue are also discussed in conjunction with the surface to volume ratio, surface defects, and cleavage planes. The dynamic nanoindentation fatigue test used in this study can be satisfactorily used to evaluate the fatigue behavior of nanoscale structures for use in MEMSyNEMS. 䊚 2002 Elsevier Science B.V. All rights reserved. Keywords: Nanoindentation; Continuous stiffness measurement; Silicon; Bending strength; Fatigue
1. Introduction Recent developments in science and engineering have advanced capability to fabricate and control structures on the scale of nanometers, and have brought problems of material behavior on the nanometer scale into the domain of engineering. Reliability studies are the key for practical application and commercialization of today’s advanced microynanoelectromechanical systems (MEMSyNEMS). Many current and potential applications for MEMSyNEMS are not really practical, because their mechanical properties have not been established, and are, to a large extent, still unknown w1–3x. Mechanical and structural aspects are of critical importance in determining long-term stability of such small structures. Precise characterization of the mechanical properties at the nanoscale is required for proper design and structureminiaturization. Recent studies have revealed that material properties are size-dependent w2,4x. However, current *Corresponding author. Tel.: q1-614-292-0651; fax: q1-614-2920325. E-mail address: [email protected] (B. Bhushan).
software developed for designing microynanoscale devices is based on bulk material properties without considering the size-dependent phenomenon. This limits the further development and application of MEMSy NEMS. Single-crystal silicon and silicon-based materials are the most common materials used in MEMSyNEMS. An early study showed silicon to be a mechanically resilient material in addition to its favorable electronic properties w5x. However, recent studies show that silicon is not good in friction and wear because of its poor fatigue properties w2,3x. Characterization of the fatigue properties is vital to designing MEMSyNEMS because moving components involved in these devices are subjected to cyclic loading. The current understanding of material fatigue is, to a large extent, based on metals. Fatigue of metals is associated with the generation and motion of dislocations and accumulation of plastic deformation. Single-crystal silicon has very limited dislocation mobility at room temperature, making the possibility of cyclic fatigue failure far less obvious w6x. It is generally accepted that in brittle materials, fatigue can only take
0257-8972/03/$ - see front matter 䊚 2002 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 7 - 8 9 7 2 Ž 0 2 . 0 0 6 6 2 - X
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place in toughened solids. However, recent studies show that single-crystal silicon thin films can degrade and fail under cyclic loading conditions in ambient air at room temperature w6,7x. Crack-growth can occur under cyclic loading conditions. Studies on fatigue of nanoscale-sized silicon structures are lacking w8x. Cyclic fatigue failure in silicon has not been well studied, especially at the nanoscale. It is uncertain if traditional fatigue theory is applicable to such small structures. A recently developed technique, continuous stiffness measurement (CSM) w9,10x, offers a significant improvement in nanoindentation testing. Load cycles used in the CSM can be used to perform fatigue tests at the nanoscale w11,12x. This paper presents an attempt to measure bending strength and fatigue properties of fixed nanoscale silicon beams. Scanning electron microscope (SEM) observations of the bending and fatigue fracture surfaces are also presented to help understand the deformation modes of the beam materials under bending and fatigue. 2. Experimental procedure 2.1. Fabrication of nanometer-scale specimens Single-crystal silicon fixed nanobeams were fabricated by bulk micromachining incorporating enhancedfield anodization using an AFM (Seiko Instruments Inc., SPA-300HV) on a (0 0 1) plane of an Si wafer separated by implanted oxygen (SIMOX) w13x. The trench (width of 6 mm) is first etched from the underside after which the top silicon dioxide (SiO2) layer is etched to expose the Si diaphragm. A line of SiO2 film with a width of less than 1-mm is deposited by field-enhanced anodization on the Si surface. This SiO2 film was used as a high-precision mask pattern for anisotropic wet etching with a solution of 20% tetra-methyl ammonium hydroxide (TMAH). It was then possible to fabricate a nanometer-scale Si structure after etching. The line pattern of SiO2 film was drawn by applying a bias voltage between an Au-coated cantileverytip and the Si diaphragm in air at room temperature. In this study, a bias voltage of 20 V and a cantilever speed of 0.4 mmys were selected, which resulted in smooth film lines as well as a film thickness higher than the 4 nm required for reliable TMAH wet etching of the Si interface on the (0 0 1) plane w13x. The Si diaphragm had an average thickness of 255 nm and hence this is the average thickness of the Si beams. Fig. 1 shows the SEM image of the Si nanobeams and a schematic of a typical nanobeam. The Si beams are oriented along the w1 1 0x direction in the (0 0 1) plane. The cross-section of the beams is trapezoidal owing to the anisotropic wet etching process. The crosssection for the beams exhibits a small amount of curvature as compared to the relatively well-defined trapezoidal shape of the Si beams due to the oxidation
Fig. 1. (a) SEM micrograph of nanobeam specimens and (b) a schematic of the shape of a typical nanobeam. The trapezoidal cross-section is due to the anisotropic wet etching during the fabrication.
process. The actual width, length and thickness values of the beams were measured using a SEM. Surface roughness measurements of the beam surfaces in tapping mode yielded a s of 0.7"0.2 nm and peak-to-valley (P–V) distance of 4"1.2 nm for Si. Prior to testing, the silicon samples were cleaned by immersing them in a ‘piranha etch’ solution (3:1 solution by volume of 98% sulphuric acid and 30% hydrogen peroxide) for 10 min to remove any organic contaminants. 2.2. Bending and fatigue tests Bending and fatigue experiments were carried out using a Nano Indenter II䉸 (MTS Systems Corp.) equipped with the CSM option. This instrument monitors and records the dynamic load and displacement of the indenter during indentation with a force resolution of approximately 75 nN and displacement resolution of approximately 0.1 nm. To avoid the indenter tip pushing into the specimen, a blunt tip should be used in the bending and fatigue tests. In this study, a diamond conical indenter with a radius of 1 mm and an included angle of 608 was used. Loading position was at the center of the span. An optical microscope with a magnification of 1500= was used to locate the center of the span. Then the specimen was moved by using a lead screw under the indenter location with a resolution
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of approximately 200 nm in longitudinal direction and less than 100 nm in lateral direction. Fig. 2 shows the schematic of bending and fatigue tests on a nanoscale Si beam using a depth-sensing nanoindenter with a harmonic force. The load is applied at the center of the span. In a rectangular beam, the maximum moments occur under the load and at the fixed ends. Due to the trapezoidal cross-section, the maximum moment (tensile bending stresses) occurs at the top surfaces at fixed ends. The CSM technique has been described in detail in Refs. w9,10x. Briefly, a harmonic force is added to the nominally increasing load, P, on the indenter. The displacement response of the indenter at the excitation frequency and the phase angle between the two are measured continuously as a function of depth. Solving for the in-phase and out-ofphase portions of the response results in an explicit determination of the contact stiffness as a continuous function of depth. The CSM technique provides load cycles of a sinusoidal shape at high frequencies that can be used to perform fatigue tests. The fatigue behavior of coatings can be studied by monitoring the change in contact stiffness since the contact stiffness is sensitive to the damage formation. To obtain deformation and damage during fatigue loading, large amplitude oscillations were used. The numbers of cycles were determined from the elapsed time. Load cycles are applied to the coating, resulting in a cyclic stress; P is the cyclic load, Pmean is the mean load, Pos is the oscillation load amplitude, and v is the oscillation frequency. All fatigue tests were conducted at an excitation frequency of 45 Hz. 3. Results and discussion 3.1. Elastic modulus and bending strength Fig. 3a shows the load–displacement curve for the Si beam that was bent to failure. The length, upper and lower widths of the beam used in the bending test are 6 mm, 400 and 800 nm, respectively. The beam showed linear behavior followed by abrupt failure. The nonlinear behavior at higher loads may result from the high surface to volume ratio of the beam. This will be discussed later. Elastic modulus and bending strength (fracture stress) of the beams can be estimated by equations based on the assumption that the beams follow linear elastic theory of an isotropic material. For a fixed elastic beam loaded at the center of the span, the elastic modulus is expressed as Es
l3 m 192I
(1)
where l is the beam length, I is the area moment of inertia for the beam cross-section and m is the slope of the load–displacement curve during bending w14x. The
Fig. 2. (a) A schematic of the bending moments generated in the beam during a bending experiment, with the load at the center of the span. (b) A schematic of the fatigue moments generated in the beam during a fatigue experiment.
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Fig. 3. (a) Load–displacement curve of a Si nanobeam (400 nm upper width, 800 nm lower width and 6 mm length) obtained from a nanoindentation experiment. (b) SEM image of the fracture surface of the beam broken during bending. (c) Bending stress distribution obtained from finite element modeling, showing that the maximum tensile stresses occur on the top surfaces near the fixed ends.
area moment of inertia is calculated from the following equation: Is
w21q4w1w2qw22 3 t, 36Žw1qw2.
(2)
where w1 and w2 are the upper and lower widths, respectively, and t is the thickness of the beam. According to linear elastic theory, for a centrally loaded beam, the moment diagram is shown in Fig. 2a. The maximum moments are generated at the ends (negative moment) and under the loading point (positive moment). Then bending stresses generated in the beam are proportional to the moments and are compressive or tensile about the neutral axis (line of zero stress). The maximum tensile stress (sb, which is the fracture stress) is produced on the top surface at both the ends and is given by w14x s bs
Fmaxle1 8I
(3)
where Fmax is the applied load at failure, l is the length of the beam and e1 is the distance of the top surface from the neutral plane of the beam cross-section and is given by w14x e 1s
tŽw1q2w2. 3Žw1qw2.
(4)
Although the moment value at the center of the beam is the same as at the ends, the tensile stresses at the center (generated on the bottom surface) are less than those generated at the ends (per Eq. (2)) because the distance from the neutral axis to the bottom surface is less than e1. This is because of the trapezoidal crosssection of the beam, which results in the neutral axis being closer to the bottom surface than the top (Fig. 2). Finite element model result shows that the maximum tensile bending stresses occurred near the ends as shown in Fig. 3c. The calculated elastic modulus and bending strength values are 187 and 17.5 GPa, respectively. Previously reported bulk elastic modulus of Si (1 1 0)
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is 169 GPa w15x and bending strength of microscale Si specimens is on the order of 6 GPa w6x. Difference in elastic modulus between the measured and reported values might result from the offset of loading from the beam center. Bending strength shows a clear specimen size dependence with nanoscale numbers being twice as large as numbers reported for larger scale specimens w6x. The offset of loading from the beam center cannot cause such high strength. High pressure can result in phase transformation in silicon. This phase transformation might contribute to the strength of the silicon beam. For the nanoscale specimens, the surface to volume ratio is much higher than for the micro- and macroscale specimens. Surface atoms can move more easily than the atoms locked in the lattice. This makes the nanoscale specimen more difficult to initiate cracks on its surface. This is probably why the nanoscale specimen has higher bending strength than the lager scale specimen. Fig. 3b shows the SEM image of the fracture surface of the beam broken during bending. The fracture surface is perpendicular to the beam length direction. The fracture surface is flat without any plastic deformation bands. This is a typical characteristic of brittle fracture. 3.2. Fatigue behavior Fig. 4a shows the contact stiffness as a function of the number of cycles for a nanoscale Si beam (upper widths380 nm, lower widths790 nm and lengths6 mm) cyclically deformed by an oscillation load amplitude of 25 mN with a mean load of 100 mN at a frequency of 45 Hz. A plateau is observed followed by an abrupt decrease in contact stiffness at 0.6=104 cycles. The abrupt decrease in contact stiffness indicates that fatigue damage has occurred, which can be used to determine fatigue life. This suggests that the failure of the beam occurs after progressive accumulation of damage, e.g. by the stable propagation of a crack. The above results show that premature fatigue occurred in nanoscale single-crystal silicon beams. The frequency used in the fatigue test (45 Hz) is much lower than the resonant frequency (55 MHz) of the beam. Therefore, the beam damage results from the cyclic loading of the indenter and not from the resonance of the beam itself. Silicon has been regarded as a brittle material. There has been no evidence of bulk silicon being susceptible to fatigue failure. This is probably because bulk tests cannot resolve the low crack-growth rates relevant to microynanoscale beams w6x. Recent studies show that micro-sized single-crystal silicon beams can degrade and fail under cyclic loading conditions in ambient air at room temperature w6,7x. In our study, the mean stress and stress amplitude are 9.8 and 2.4 GPa, respectively. The maximum stress (12.2 GPa) is 30% lower than the bending strength (fracture stress). The fatigue fracture
Fig. 4. (a) Contact stiffness as a function of the number of cycles for a Si nanobeam (380 nm upper width, 790 nm lower width and 6 mm length) cyclically deformed by an oscillation load amplitude of 25 mN with a mean load of 100 mN at a frequency of 45 Hz. (b) SEM image of the fracture surface of the beam broken during fatigue, indicating cleavage steps.
surface is rough with steps, as shown in Fig. 4b. This indicates that initiation and propagation of the fatigue cracks oriented during failure. However, it is difficult to correlate the growth of cracks from the fracture surface. The steps at the fatigue fracture surface result from the transition in crack path manifesting itself in terms of dissipating energy w6x. Flaws on the beam surface can be fatigue sources w6,7x. Native oxide (SiO2) layer forms on the Si beam surface upon reaction with the atmosphere. More SiO2 can form at the flaws where surface stress is relatively higher than other places. SiO2 has much lower bending strength (7.6 GPa) and fracture toughness (0.6 MPa m1y2) than single-crystal silicon (bending strengths17 GPa; fracture toughnesss 1.7 MPa m1y2) w8x. During the fatigue test, cracks can initiate in the SiO2 layer at the flaw sites. At room temperature, dislocation activity is very low in singlecrystal silicon. The dominant failure mode is cleavage. The morphology of the step-like surface is a direct result of the crystallography of cleavage. It is well known that the {1 1 1} planes are cleavage planes for single-crystal silicon. Cleavage steps form on {1 1 1} fracture surfaces as a means of dissipating energy during failure w6x. These cracks tend to propagate by cracking along multiple {1 1 1} cleavage planes to form steps. It has
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been reported that high pressure can cause phase transformation in single-crystal silicon. The phase transformation can induce localized stressystrain, which may assist cracks in initiation and propagation. This study clearly demonstrates that fatigue properties of nanoscale specimens can be studied by using the CSM technique.
this research was provided by the National Science Foundation (Contract No. ECS-9820022). The content of this information does not necessarily reflect the position or policy of the Government and no official endorsement should be inferred. References
4. Conclusions A technique to perform bending and fatigue tests of nanometer scale fixed beam specimens made of singlecrystal silicon using a depth-sensing nanoindenter with a harmonic force has been described. The nanoscale beams exhibited higher bending strength than the larger scale specimens. Load cycles used in the CSM were used to study the fatigue properties of nanoscale Si beams. Fatigue behavior of the beams was monitored by a change in the contact stiffness. Cleavage steps were found on the fatigue fracture surface. The nanoindentation bending and fatigue tests used in this study can be satisfactorily used to evaluate the bending strength and fatigue properties of nanoscale structures for use in MEMSyNEMS. Acknowledgments The nanobeam samples were prepared by T. Namazu and Prof. Y. Isono of the Department of Mechanical Engineering at Ritsumeikan University, Japan. The authors would like to thank Nano Innovation Center, MTS Corporation, TN for technical support and Dr S. Sundararajan for engaging in several useful discussions during the course of this study. Financial support for
w1x B. Bhushan (Ed.), Tribology Issues and Opportunities in MEMS, Kluwer Academic Publishers, Dordrecht, Netherlands, 1998. w2x B. Bhushan, Handbook of MicroyNanotribology, second ed., CRC, Boca Raton, FL, 1999. w3x B. Bhushan, Modern Tribology Handbook, vol. 1—Principles of Tribology; vol. 2—Materials, Coatings, and Industrial Applications, CRC Press, Boca Raton, FL, 2001. w4x B. Bhushan, A.V. Kulkarni, W. Bonin, J.T. Wyrobek, Phil. Mag. A 74 (1996) 1117–1128. w5x K.E. Petersen, Proc. IEEE 70 (1982) 420. w6x C.L. Muhlstein, S.B. Brown, R.O. Ritche, J. Microelectromech. Syst. 10 (2001) 593–600. w7x T. Ando, M. Shikida, K. Sato, Sensors and Actuators A 93 (2000) 70–75. w8x S. Sundararajan, B. Bhushan, Sensors and Actuators 48 (2002) 11–36. w9x J.B. Pethica, W.C. Oliver, Thin films: stresses and mechanical properties, in: J.C. Bravman, W.D. Nix, D.M. Barnett, D.A. Smith, (Eds.), Mat. Res. Soc., Pittsburgh, 130 (1989) 13–23. w10x W.C. Oliver, G.M. Pharr, J. Mater. Res. 7 (1992) 1564–1583. w11x X. Li, B. Bhushan, Mater. Charact., 48 (2002) 11–36. w12x X. Li, B. Bhushan, J. Appl. Phys. 91 (2002) 8334–8336. w13x T. Namazu, Y. Isono, T. Tanaka, J. Microelectromech. Syst. 9 (2000) 450–459. w14x R.J. Roark, Formulas for Stress and Strain, McGraw-Hill, New York, 1965. w15x B. Bhushan, S. Venkatesan, Adv. Info. Storage Syst. 5 (1993) 211–239.