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͑ a ͒ S-shaped beams are attached over a long length d . ͑ b ͒ Arc- shaped beams are attached only very near their tips, see Ref. 6.
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This paper presents a study of adhesion energies that are relevant to Au-Au microswitch contacts at the nano- and micronscales. Adhesion measurements are obtained from cantilevered Au microelectromechanical system (MEMS) microswitch structures with varying lengths. Scanning electron microscopy measurements of the microbeam profiles are combined wit...
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Context 1
... recent years, there has been increasing interest in de- veloping an understanding of adhesion phenomena at the 1–9 nano- and microscales. These have been motivated largely by adhesion-related failure in microelectromechanical sys- tems ͑ MEMSs ͒ , such as microswitches that are being used 3–5 increasingly in commercial and military approaches. In many cases, these devices are fabricated from Au, due largely to the inertness of Au and the absence of surface 10 oxides on Au. However, adhesion-related phenomena can still occur in Au MEMS structures. Such adhesion-related failures may occur during the fabrication process or in field 3–5 operation. In such scenarios, adhesion may occur when the capillary forces from the wet etching environment bring the compliant structures into contact with the substrate. If the adhesion energy is sufficient to balance the stored elastic energy in the deflected member, then the structure will ad- here to the substrate, even after the external force is re- moved. At the nanoscale, the so-called Derjaguin-Muller- Toporov ͑ DMT ͒ and Johnson-Kendall-Roberts ͑ JKR ͒ models 7–9,11–14 have been used successfully to characterize adhesion. 1–4 6 Mastrangelo and co-worker, and de Boer and Michalske have also established a theoretical framework for the modeling of adhesion in cantilevered MEMS structures. These have been complemented by experimental work by de Boer 6 and Michalske. However, most of the prior work has focused largely on fundamental studies of adhesion in silicon 2–5 MEMS structures. Hence, as Au MEMS structures have emerged in a number of commercial and military MEMS applications, there is a need for fundamental studies of adhesion in Au MEMS structures. The adhesion energy represents the fundamental quantity that must be established in basic studies of adhesion at the micro- and nanoscales. However, various researchers have reported significant differences between the adhesion ener- 8,15 gies at the micro- and nanoscales. This paper explores the fundamental reasons for the observed differences between the nano- and micron-scales adhesion energy measurements, and shows that the differences can be partially attributed to the shielding due to contact between surface asperities. This paper is divided into six sections. In Sec. II, the theoretical framework for the micron- and nanoscale experiments is presented. This is followed by Sec. III in which the micron- and nanoscale experimental procedures are described. The numerical modeling of the Au MEMS structures ͑ used in the micron-scale experiments ͒ is then presented in Sec. IV, before discussing the results of the combined experimental, theoretical, and computational studies in Sec. V. Salient con- clusions arising from this study are summarized in Sec. VI. In studying the adhesion of suspended beam structures, 1,2 Mastrangelo and Hsu had proposed two adhesion configurations, the S-shaped and arc-shaped adhesions. The cross- sectional views of these two configurations were shown in Fig. 1. In Fig. 1 ͑ a ͒ , a cantilever beam of length L , thickness t , and height h is adhering to its substrate a distance d = ͑ L − s ͒ from its tip. This is the S-shaped configuration. The arc-shaped adhesion configuration is illustrated in Fig. 1 ͑ b ͒ , where only the tip of the beam is adhered to the substrate. The total energy of the system is the sum of the elastic energy stored in the beam due to the bending, plus the interfacial adhesion energies of the contact area. 6 EIh 2 U = U + U = − ⌫ w ͑ L − s ͒ , ͑ 1 ͒ where w and E are the width and Young’s modulus of the beam, respectively, ⌫ is the adhesion energy, and I is the 6 second moment of area. de Boer and Michalske further considered this adhesion problem from a fracture mechanics per- spective: The detached length s could be thought of as the “crack length.” Hence the restoring elastic energy stored in the beam is the “crack driving force,” while the adhesion energy ⌫ is the “crack resistance.” For clean smooth surfaces, ⌫ should be twice of the surface energy of the beam and the substrate material, when they are made from the same material. The total energy U T ͑ s ͒ of the system, plotted in Fig. 2, has a single minimum corresponding to the equilibrium s . This is found by setting dU T / ds = 0 to obtain s = ͩ 3 Et 3 h 2 ͪ 1/4 . ͑ 2 ͒ 2 ⌫ The energy curve has a single equilibrium point if s Ͻ L and no equilibrium point if s Ͼ L . Thus the beam is pinned to the substrate if s Ͻ L , and it is free if s Ͼ L . Equation ͑ 2 ͒ was obtained without considering the shear deformations of the tip of the beam, so it was applied to S-shaped beams. However, for arc-shaped beams, the shear deformation is important at the tip of the beam. Hence, modifying the boundary condition to include the effects of shear deformation gives the minimum detachment length for 6 an arc-shaped beam to be s = ͩ 3 Et 3 h 2 ͪ 1/4 . ͑ 3 ͒ 8 ⌫ The adhesion energy, ⌫ , can be obtained by rearranging Eqs. ͑ 2 ͒ and ͑ 3 ͒ . This gives ⌫ = 2 3 ͩ Et s 3 4 h 2 ͪ for S-shaped beams, ͑ 4 ͒ 3 Et h ⌫ = 8 s 4 for arc-shaped beams. ͑ 5 ͒ Hence, the adhesion energy can be determined by measuring the detachment length of beams in cantilevered structures with known geometries and elastic properties. It is important to note here that the above models assumed that the beam deflections occurred solely in the elastic regime. They also assume that attractive forces operate only between the contact portions of the interfacial area. Further more, for perfectly smooth beams and substrates, the measured adhesion energy should be twice the surface energy. However, the adhesion energy is also affected by surface roughness. The Maugis-Dugdale MD theory provides analytical solutions describing the contact between two adhesive elastic spheres that falls in the intermediate case between the JKR ͑ Ref. 17 ͒ and DMT ͑ Ref. 18 ͒ models. The JKR model applies to contact of soft materials with strong adhesion forces and large tip radii, while the DMT model applies to stiff materials with weak adhesion forces and small tip radii. However, the MD model requires cumbersome numerical computation when applying to the interpretation of experimental data from scanning force microscopy. In this study, a general equation was used to describe the functional relationship between the elastic indentation depth and the normal applied load. This equation was developed 19 originally by Pietrement and Troyon. It was then modified 12 in subsequent work by Carpick et al. , who showed that it approximated the MD model to within an accuracy of 1% or better. The MD model defines a nondimensional parameter, , that is given ...
Context 2
... recent years, there has been increasing interest in de- veloping an understanding of adhesion phenomena at the 1–9 nano- and microscales. These have been motivated largely by adhesion-related failure in microelectromechanical sys- tems ͑ MEMSs ͒ , such as microswitches that are being used 3–5 increasingly in commercial and military approaches. In many cases, these devices are fabricated from Au, due largely to the inertness of Au and the absence of surface 10 oxides on Au. However, adhesion-related phenomena can still occur in Au MEMS structures. Such adhesion-related failures may occur during the fabrication process or in field 3–5 operation. In such scenarios, adhesion may occur when the capillary forces from the wet etching environment bring the compliant structures into contact with the substrate. If the adhesion energy is sufficient to balance the stored elastic energy in the deflected member, then the structure will ad- here to the substrate, even after the external force is re- moved. At the nanoscale, the so-called Derjaguin-Muller- Toporov ͑ DMT ͒ and Johnson-Kendall-Roberts ͑ JKR ͒ models 7–9,11–14 have been used successfully to characterize adhesion. 1–4 6 Mastrangelo and co-worker, and de Boer and Michalske have also established a theoretical framework for the modeling of adhesion in cantilevered MEMS structures. These have been complemented by experimental work by de Boer 6 and Michalske. However, most of the prior work has focused largely on fundamental studies of adhesion in silicon 2–5 MEMS structures. Hence, as Au MEMS structures have emerged in a number of commercial and military MEMS applications, there is a need for fundamental studies of adhesion in Au MEMS structures. The adhesion energy represents the fundamental quantity that must be established in basic studies of adhesion at the micro- and nanoscales. However, various researchers have reported significant differences between the adhesion ener- 8,15 gies at the micro- and nanoscales. This paper explores the fundamental reasons for the observed differences between the nano- and micron-scales adhesion energy measurements, and shows that the differences can be partially attributed to the shielding due to contact between surface asperities. This paper is divided into six sections. In Sec. II, the theoretical framework for the micron- and nanoscale experiments is presented. This is followed by Sec. III in which the micron- and nanoscale experimental procedures are described. The numerical modeling of the Au MEMS structures ͑ used in the micron-scale experiments ͒ is then presented in Sec. IV, before discussing the results of the combined experimental, theoretical, and computational studies in Sec. V. Salient con- clusions arising from this study are summarized in Sec. VI. In studying the adhesion of suspended beam structures, 1,2 Mastrangelo and Hsu had proposed two adhesion configurations, the S-shaped and arc-shaped adhesions. The cross- sectional views of these two configurations were shown in Fig. 1. In Fig. 1 ͑ a ͒ , a cantilever beam of length L , thickness t , and height h is adhering to its substrate a distance d = ͑ L − s ͒ from its tip. This is the S-shaped configuration. The arc-shaped adhesion configuration is illustrated in Fig. 1 ͑ b ͒ , where only the tip of the beam is adhered to the substrate. The total energy of the system is the sum of the elastic energy stored in the beam due to the bending, plus the interfacial adhesion energies of the contact area. 6 EIh 2 U = U + U = − ⌫ w ͑ L − s ͒ , ͑ 1 ͒ where w and E are the width and Young’s modulus of the beam, respectively, ⌫ is the adhesion energy, and I is the 6 second moment of area. de Boer and Michalske further considered this adhesion problem from a fracture mechanics per- spective: The detached length s could be thought of as the “crack length.” Hence the restoring elastic energy stored in the beam is the “crack driving force,” while the adhesion energy ⌫ is the “crack resistance.” For clean smooth surfaces, ⌫ should be twice of the surface energy of the beam and the substrate material, when they are made from the same material. The total energy U T ͑ s ͒ of the system, plotted in Fig. 2, has a single minimum corresponding to the equilibrium s . This is found by setting dU T / ds = 0 to obtain s = ͩ 3 Et 3 h 2 ͪ 1/4 . ͑ 2 ͒ 2 ⌫ The energy curve has a single equilibrium point if s Ͻ L and no equilibrium point if s Ͼ L . Thus the beam is pinned to the substrate if s Ͻ L , and it is free if s Ͼ L . Equation ͑ 2 ͒ was obtained without considering the shear deformations of the tip of the beam, so it was applied to S-shaped beams. However, for arc-shaped beams, the shear deformation is important at the tip of the beam. Hence, modifying the boundary condition to include the effects of shear deformation gives the minimum detachment length for 6 an arc-shaped beam to be s = ͩ 3 Et 3 h 2 ͪ 1/4 . ͑ 3 ͒ 8 ⌫ The adhesion energy, ⌫ , can be obtained by rearranging Eqs. ͑ 2 ͒ and ͑ 3 ͒ . This gives ⌫ = 2 3 ͩ Et s 3 4 h 2 ͪ for S-shaped beams, ͑ 4 ͒ 3 Et h ⌫ = 8 s 4 for arc-shaped beams. ͑ 5 ͒ Hence, the adhesion energy can be determined by measuring the detachment length of beams in cantilevered structures with known geometries and elastic properties. It is important to note here that the above models assumed that the beam deflections occurred solely in the elastic regime. They also assume that attractive forces operate only between the contact portions of the interfacial area. Further more, for perfectly smooth beams and substrates, the measured adhesion energy should be twice the surface energy. However, the adhesion energy is also affected by surface roughness. The Maugis-Dugdale MD theory provides analytical solutions describing the contact between two adhesive elastic spheres that falls in the intermediate case between the JKR ͑ Ref. 17 ͒ and DMT ͑ Ref. 18 ͒ models. The JKR model applies to contact of soft materials with strong adhesion forces and large tip radii, while the DMT model applies to stiff materials with weak adhesion forces and small tip radii. However, the MD model requires cumbersome numerical computation when applying to the interpretation of experimental data from scanning force microscopy. In this study, a general equation was used to describe the functional relationship between the elastic indentation depth and the normal applied load. This equation was developed 19 originally by Pietrement and Troyon. It was then modified 12 in subsequent work by Carpick et al. , who showed that it approximated the MD model to within an accuracy of 1% or better. The MD model defines a nondimensional parameter, , that is given ...
Context 3
... recent years, there has been increasing interest in de- veloping an understanding of adhesion phenomena at the 1–9 nano- and microscales. These have been motivated largely by adhesion-related failure in microelectromechanical sys- tems ͑ MEMSs ͒ , such as microswitches that are being used 3–5 increasingly in commercial and military approaches. In many cases, these devices are fabricated from Au, due largely to the inertness of Au and the absence of surface 10 oxides on Au. However, adhesion-related phenomena can still occur in Au MEMS structures. Such adhesion-related failures may occur during the fabrication process or in field 3–5 operation. In such scenarios, adhesion may occur when the capillary forces from the wet etching environment bring the compliant structures into contact with the substrate. If the adhesion energy is sufficient to balance the stored elastic energy in the deflected member, then the structure will ad- here to the substrate, even after the external force is re- moved. At the nanoscale, the so-called Derjaguin-Muller- Toporov ͑ DMT ͒ and Johnson-Kendall-Roberts ͑ JKR ͒ models 7–9,11–14 have been used successfully to characterize adhesion. 1–4 6 Mastrangelo and co-worker, and de Boer and Michalske have also established a theoretical framework for the modeling of adhesion in cantilevered MEMS structures. These have been complemented by experimental work by de Boer 6 and Michalske. However, most of the prior work has focused largely on fundamental studies of adhesion in silicon 2–5 MEMS structures. Hence, as Au MEMS structures have emerged in a number of commercial and military MEMS applications, there is a need for fundamental studies of adhesion in Au MEMS structures. The adhesion energy represents the fundamental quantity that must be established in basic studies of adhesion at the micro- and nanoscales. However, various researchers have reported significant differences between the adhesion ener- 8,15 gies at the micro- and nanoscales. This paper explores the fundamental reasons for the observed differences between the nano- and micron-scales adhesion energy measurements, and shows that the differences can be partially attributed to the shielding due to contact between surface asperities. This paper is divided into six sections. In Sec. II, the theoretical framework for the micron- and nanoscale experiments is presented. This is followed by Sec. III in which the micron- and nanoscale experimental procedures are described. The numerical modeling of the Au MEMS structures ͑ used in the micron-scale experiments ͒ is then presented in Sec. IV, before discussing the results of the combined experimental, theoretical, and computational studies in Sec. V. Salient con- clusions arising from this study are summarized in Sec. VI. In studying the adhesion of suspended beam structures, 1,2 Mastrangelo and Hsu had proposed two adhesion configurations, the S-shaped and arc-shaped adhesions. The cross- sectional views of these two configurations were shown in Fig. 1. In Fig. 1 ͑ a ͒ , a cantilever beam of length L , thickness t , and height h is adhering to its substrate a distance d = ͑ L − s ͒ from its tip. This is the S-shaped configuration. The arc-shaped adhesion configuration is illustrated in Fig. 1 ͑ b ͒ , where only the tip of the beam is adhered to the substrate. The total energy of the system is the sum of the elastic energy stored in the beam due to the bending, plus the interfacial adhesion energies of the contact area. 6 EIh 2 U = U + U = − ⌫ w ͑ L − s ͒ , ͑ 1 ͒ where w and E are the width and Young’s modulus of the beam, respectively, ⌫ is the adhesion energy, and I is the 6 second moment of area. de Boer and Michalske further considered this adhesion problem from a fracture mechanics per- spective: The detached length s could be thought of as the “crack length.” Hence the restoring elastic energy stored in the beam is the “crack driving force,” while the adhesion energy ⌫ is the “crack resistance.” For clean smooth surfaces, ⌫ should be twice of the surface energy of the beam and the substrate material, when they are made from the same material. The total energy U T ͑ s ͒ of the system, plotted in Fig. 2, has a single minimum corresponding to the equilibrium s . This is found by setting dU T / ds = 0 to obtain s = ͩ 3 Et 3 h 2 ͪ 1/4 . ͑ 2 ͒ 2 ⌫ The energy curve has a single equilibrium point if s Ͻ L and no equilibrium point if s Ͼ L . Thus the beam is pinned to the substrate if s Ͻ L , and it is free if s Ͼ L . Equation ͑ 2 ͒ was obtained without considering the shear deformations of the tip of the beam, so it was applied to S-shaped beams. However, for arc-shaped beams, the shear deformation is important at the tip of the beam. Hence, modifying the boundary condition to include the effects of shear deformation gives the minimum detachment length for 6 an arc-shaped beam to be s = ͩ 3 Et 3 h 2 ͪ 1/4 . ͑ 3 ͒ 8 ⌫ The adhesion energy, ⌫ , can be obtained by rearranging Eqs. ͑ 2 ͒ and ͑ 3 ͒ . This gives ⌫ = 2 3 ͩ Et s 3 4 h 2 ͪ for S-shaped beams, ͑ 4 ͒ 3 Et h ⌫ = 8 s 4 for arc-shaped beams. ͑ 5 ͒ Hence, the adhesion energy can be determined by measuring the detachment length of beams in cantilevered structures with known geometries and elastic properties. It is important to note here that the above models assumed that the beam deflections occurred solely in the elastic regime. They also assume that attractive forces operate only between the contact portions of the interfacial area. Further more, for perfectly smooth beams and substrates, the measured adhesion energy should be twice the surface energy. However, the adhesion energy is also affected by surface roughness. The Maugis-Dugdale MD theory provides analytical solutions describing the contact between two adhesive elastic spheres that falls in the intermediate case between the JKR ͑ Ref. 17 ͒ and DMT ͑ Ref. 18 ͒ models. The JKR model applies to contact of soft materials with strong adhesion forces and large tip radii, while the DMT model applies to stiff materials with weak adhesion forces and small tip radii. However, the MD model requires cumbersome numerical computation when applying to the interpretation of experimental data from scanning force microscopy. In this study, a general equation was used to describe the functional relationship between the elastic indentation depth and the normal applied load. This equation was developed 19 originally by Pietrement and Troyon. It was then modified 12 in subsequent work by Carpick et al. , who showed that it approximated the MD model to within an accuracy of 1% or better. The MD model defines a nondimensional parameter, , that is given ...
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Citations
... The model has since been used subsequently in Refs. 19,36, and 37 to model contact around dust particles in organic electronic structures. ...
This paper presents the results of a combined analytical, computational, and experimental study of adhesion and degradation of Organic Light Emitting Devices (OLEDs). The adhesion between layers that are relevant to OLEDs is studied using an atomic force microscopy technique. The interfacial failure mechanisms associated with blister formation in OLEDs and those due to the addition of TiO2 nanoparticles into the active regions are then elucidated using a combination of fracture mechanics, finite element modeling and experiments. The blisters observed in the models are shown to be consistent with the results from adhesion, interfacial fracture mechanics models, and prior reports of diffusion-assisted phenomena. The implications of the work are then discussed for the design of OLED structures with improved lifetimes and robustness.
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... The definition of this adhesive-contact law constitutes the micro-scale. In this paper, this adhesive contact-distance curve of two rough surfaces interacting was established from a combination of R q (nm) σ s (nm) R (μm) N (μm -2 ) E (GPa) [14] ν [14] Greenwood-Williamson asperity model and Maugis transition's theory. ...
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