Design of metal interconnects for stretchable ... - Semantic Scholar
Microelectronics Reliability 48 (2008) 825–832
Contents lists available at ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel
Design of metal interconnects for stretchable electronic circuits Mario Gonzalez a,*, Fabrice Axisa b, Mathieu Vanden Bulcke a, Dominique Brosteaux c, Bart Vandevelde a, Jan Vanfleteren b,c a
IMEC, IPSI/REMO, Kapeldreef 75, 3001 Leuven, Belgium TFCG Microsystems, IMEC, Gent-Zwijnaarde, Belgium c ELIS – TFCG Microsystems, University of Ghent, Gent-Zwijnaarde, Belgium b
a r t i c l e
i n f o
Article history: Received 28 September 2007 Received in revised form 29 January 2008 Available online 5 June 2008
a b s t r a c t The trend of microelectronic products in the textile or medical field is toward higher functionality, miniaturization, application of new materials and a necessity for deformable electronic circuits for improving the comfort control. In this work, the design of flexible and stretchable interconnections is presented. These interconnections are done by embedding sinuous electroplated metallic wires in a stretchable substrate material. A silicone material was chosen as substrate because of its low stiffness and high elongation before break. Common metal conductors used in the electronic industry have very limited elastic ranges; therefore a metallization design is crucial to allow stretchability of the conductors going up to 100%. Different configurations were simulated and compared among them and based on these results, a horseshoe like shape was suggested. This design allows a large deformation with the minimum stress concentration. Moreover, the damage in the metal is significantly reduced by applying narrow metallization schemes. In this way, each conductor track has been split in four parallel lines of 15 lm and 15 lm space in order to improve the mechanical performance without limiting the electrical characteristics. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Flexible and stretchable electronic circuits is a relatively new concept aiming in a first instance at improving the comfort of consumer’s needs. This technology can also be used in many other applications where the ability to deform is an advantage or where the electronics should preferably take the shape of the object in which they are integrated. Some examples of this technology are skin mounted or implantable biomedical devices [1,2] where the circuit must behave as the tissue itself and textile or wearable electronics [3,4]. Traditional signal and power transmission lines in microelectronic systems are placed on rigid or at most flexible substrates, thus limiting the commercial applications to relatively small devices for optimal mobility and comfort. Stretchable electronic circuits will integrate different components onto a compliant polymer substrate that may be stretched once or many times depending on the application. One way to make these circuits is to place rigid or flexible components distributed over a polymer surface and then interconnect these components with a stretchable connection. Nevertheless, one of the critical points in this technology is the reliability of the elastic interconnections. This is particularly challenging given the relatively high and complex * Corresponding author. Tel.: +32 16 28 86 02. E-mail address: [email protected] (M. Gonzalez). 0026-2714/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.microrel.2008.03.025
mechanical loading expected for these applications, i.e. bending, elongation and torsion. Several technologies have been proposed in recent years such as intrinsic conductive polymers [5,6], pre-stressed metal conductors [7–9] or in plane patterned metal conductors [10,11]. Nowadays, metals are the best options to realize these interconnections because of their high electrical performance and relatively low cost. However, in all cases, the main challenge is maintaining the integrity of the circuit during and after flexing or stretching the substrate. In this work, a description of a molded interconnect device (MID) technology is given and the shape of metal interconnections is optimized by finite element analysis (FEA) to allow large deformations. The interconnection between two points will not be a straight line but a periodic undulating metal track. In this way a sort of two-dimensional spring is obtained. As stretchable polymer we use polydimethylsiloxanes (PDMS) because their low elastic modulus and high stretchability. Moreover, PDMS has been used in many medical implantable devices and also in electronics it is not a new material [12]. As a first step, the 3D FEM simulations were used to compare the performance of different shapes (sinus, ‘‘U” shape, half circles, elliptical and ‘‘horseshoe”) and identify the more promising structures that later will be mechanically tested and optimized. The outcome of thermo-mechanical modeling is presented as a stress or strain distribution in the different parts of the structure. The quantification
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M. Gonzalez et al. / Microelectronics Reliability 48 (2008) 825–832
Fig. 1 outlines the sample fabrication. All processing is done on flexible but non-stretchable substrate which allows using conventional electroplating techniques. In a first instance, a photoresist is spin-coated on a copper foil and patterned, with the meandering shape by UV-radiation. Then a 4 lm thick gold layer was electroplated, followed by a 2 lm nickel layer to improve solderability. Gold was chosen as metal conductor to facilitate the separation of the sacrificial copper foil. However, other metals can be used if an extra thin metal layer is applied on top of the copper foil. Before etching the copper foil, the conductors are encapsulated with 0.25 or 0.5 mm thick elastic polymer. As elastic polymer material Silastic MDX4-4210 from Dow Corning had been chosen because it’s a biomedical grade silicone elastomer with a low Young’s modulus and high elongation (up to 470% from supplier datasheet). More detailed information about this processing was presented by Brosteaux [13].
of an appropriate shape is crucial to allow stretchability of the conductors. For this first approach a 2D plane-stress model was done. The objective of this preliminary study is to compare the stresses induced in a copper conductor when a 20% deformation is applied in the axial direction of the meander. The effect of the substrate was neglected in a first instance. The conductor used for these models is copper with a thickness of 15 lm and a trace width of 90 lm. An amplitude of 700 lm and a period of 500 lm was used for the three proposed configurations (Fig. 2). The mechanical behavior of the copper was modeled as being isotropic, perfect plastic and temperature independent with a Young’s modulus of 117 GPa and an Yield Stress of 172.3 MPa. In a 3D simulation of these configurations an out of plane deformation is observed when a load or displacement is applied in the axial direction (Fig. 3). However, in an actual configuration the metal conductor is embedded into a stretchable substrate and the out of plane deformation is constrained. Therefore, even if a 2D plane stress (in plane deformation) model is not an accurate method because the effects of substrate and metal thickness and the out of plane deformation are not taken into account, it is a good ‘‘first view” of the stresses induced in the structure.
3. Preliminary elastic model
3.1. Deformation analysis of different conductor shapes
Even if simple conductor shapes like triangular or sinusoidal allow higher deformations compared to a straight line, they present a high concentration of stresses in some regions, giving rise to early failures at fairly small deformations. Common metal conductors (Au, Cu, Ni, Pt) have very limited elastic ranges, therefore a design
Three different conductor shapes were analyzed and compared. In all cases, a total deformation of 20% was applied in the axial direction of the meander. Results of these models are presented graphically in Fig. 4. In the case of an elliptical shape (Fig. 4A), a high stress and strain concentration is observed in the crest and trough of the line. In the inner radius, tensile stresses are present, while in the outer radius, compressive stresses are observed. In order to avoid this stress concentration a higher radius of curvature is preferred. The ‘‘U” shape (Fig. 4B) offers a better strain distribution but is still limited by a reduced radius of curvature. Furthermore the straight vertical lines limit the deformation perpendicular to the axis of the meander when a biaxial deformation is needed. In the optimal shape (Fig. 4C); the stress is distributed in an extended part of the conductor. A reduction of 39.2% in the plastic strain is obtained with this shape regarding the elliptical one. As we are just looking for trends, an ‘‘A to B” strain comparison is enough for choosing the conductor shape. Predominant failures are expected in regions where the highest plastic strain concentration is located. Increasing the amplitude of the wave will also reduce the accumulated strain; however, we are limited by the maximum path length allowed for routing. In order to reduce even more the strains in the metal conductor, without sacrificing the electrical performance and/or changing the amplitude or period of the design, the line can be subdivided in several lines of smaller width as shown in Fig. 5. This ‘‘multi-copper trace” improves the stretchability and reduces the induced stresses. In an idealized case (without substrate) for the geometry proposed here, the strains are reduced from 5.25% to only 0.011% if the copper line width is reduced from 90 lm to 10 lm.
of the stresses and strains is based on the substrate stiffness, the width of the metal track and the radius of curvature of these conductors. 2. Sample preparation
Photoresits
Copper Foil 1. Spin coat photoresist 2. Pattern Photoresist
3. Plate metal (Cu, Au, Pt, Ni)
Metal
4. Dissolve Photoresis t
PDMS PDMS 5. Overmould PDMS 6. Etch sacrificial copper foil
7. Invert sample and overmould PDMS Fig. 1. Process sequence for metallic stretchable interconnections embedded in PDMS.
4. FEM simulation of the conductor embedded into the stretchable substrate In order to quantify the strains in the copper meander, the substrate has to be included. When the substrate is stretched in the axial direction, due to the Poisson’s effect, the tensile deformation is always accompanied by a lateral contraction as shown in Fig. 6. During a uniaxial stretching, global and local deformations are observed. Globally, the copper conductor is under tension when the line is parallel to the stretching direction and is under compression
M. Gonzalez et al. / Microelectronics Reliability 48 (2008) 825–832
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Fig. 2. Different conductor shapes for metallic stretchable interconnections embedded in a stretchable matrix.
Fig. 3. Out of plane deformation of an unconstrained copper meander stretched 20%.
when the copper trace is perpendicular to the stretching direction. Locally, the inner part of the copper trace is in tension and the outer part in compression. The magnitude of the strains caused by the local or global deformation depends on the stiffness of the substrate and the thickness of the copper trace. The dashed line in Figs. 6 and 7 indicate the original dimensions of the structure. From these images it is seen that the accumulated plastic strain for the
multi-track design is more than six times smaller than the original single track design. We have to underline that the conductor shape is optimized for a uniaxial deformation in the direction of the conductor. Other complex deformation such as biaxial and torsion are under investigation. A qualitative comparison between modeling and experiments shows that calculated regions with high concentration of plastic
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Fig. 4. Plastic strain distribution in copper conductor line for three different conductor shapes. (A) Elliptical shape; (B) ‘‘U” shape; (C) horseshoe shape.
strain ðepl max ffi 10%Þ correspond to the observed failures (Fig. 8). Visible cracks are observed in the crests and troughs of the meander at about 25% of total deformation. Because the copper conductor is completely embedded into the stretchable matrix, 2D plane stress or plane strain models cannot
be used. Those models assume a unique material in the thickness direction. For solving this problem 3D FEM has to be used. However, 3D models require high number of memory and computational time. The same 3D effect can be obtained by using composite shell elements. Those elements are composed of layers
M. Gonzalez et al. / Microelectronics Reliability 48 (2008) 825–832
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Fig. 5. Plastic strain distribution in a multi-track horseshoe conductor design.
Fig. 6. Poisson effect observed during a uniaxial tension test for a single conductor line. Dashed line shows the original dimensions of the substrate.
of different materials with various layer thicknesses. Furthermore, the material in each layer may be linear or not linear. Therefore, gold or copper can be modeled as a perfect plastic material. In order to validate the accuracy of the 2D composite elements, a horseshoe meander was modeled by using 3D brick elements and 2D composite shell elements. In both cases, the PDMS material was modeled as a hyperelastic material. A Neo-Hooke model (C10 = 0.157 MPa) gives an acceptable fit for nominal strain levels up to 100%. Results of this comparison are depicted in Fig. 9. The continuous line shows the strains calculated with the 3D model and the points represent the plastic strain calculated in the copper meander by using composite 2D elements. As the difference between 2D and 3D elements is negligible and calculation time was divided by 10 it is advisable to use 2D composite shell elements to model these structures. The deformation of the patterned metal conductor is, in a certain manner, controlled by the deformation of the stretchable substrate. If the conductor is embedded in a stiff substrate, the deformation of the conductor will be the same as the one of the substrate. On the other hand, if a very soft substrate is used, the conductor has some ‘‘freedom” to move inside the substrate,
reducing in this way the Poisson’s effect and in consequence, the accumulated plastic strain (compressive stresses are reduced). To quantify the maximum strain in the conductor as a function of the stiffness of the substrate, the meander design presented in Fig. 6 was modeled with different Young’s modulus of the substrate. For this comparative study the substrate is modeled as a linear elastic material with a Young’s modulus varying from 5 to 150 MPa. In this case, the thickness of copper and substrate were kept constant with values of 17 lm and 100 lm respectively. Results of this study are presented in Fig. 10. For this configuration, when the Young’s Modulus of the substrate is about 120 MPa, the plastic strain in the copper is practically the same as the total strain applied to the substrate. This means, that increasing the stiffness of the substrate will decrease the maximum allowable stretchability of the structure without electrical failure.
5. Parameters used in the horseshoe design The horseshoe pattern is created by joining a series of circular arcs as shown in Fig. 11, where R is the inner radius, W is the width
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M. Gonzalez et al. / Microelectronics Reliability 48 (2008) 825–832
Fig. 7. Poisson effect observed during a uniaxial tension test for a multiple conductor line. Dashed line shows the original dimensions of the substrate.
Fig. 8. Tensile strain test of horseshoe metal interconnects embedded into a Sylgard 186 PDMS matrix. (a) Before elongation, (b) After 25% elongation highlighting the failures in the crest and trough.
14
zone 2
10
20
Max. Eq. Plastic Strain (%)
Eq. Plastic Strain (-)
Zone 1 - 3D Zone 2 - 3D Zone 1 - 2D Zone 2 - 2D
zone 1
12
8 6 4 2
15
10 t Cu = 17 µm t subs = 100 µm Total deformation = 20%
5
0 0
5
10
15
20
25
30
Total deformation (%)
0 0
20
40
60
80
100
120
140
160
Young's Modulus of Substrate (MPa) Fig. 9. Comparison of the equivalent plastic strain induced in the copper conductor embedded into a PDMS matrix as function of the applied deformation. Thickness of copper: 17 lm; thickness of PDMS: 100 lm.
Fig. 10. Equivalent plastic strain induced in the copper as function of the Young’s Modulus of the substrate.
831
R θ
θ=0º
w
θ=45º Fig. 11. Definition of horseshoe design by its inner radius (R), joining angle (h) and width of the metal track (w).
2.5 2.0 1.5 1.0
Θ =0 Θ=30
0.5
Θ=45
0.0 50
60
70
80
90
100
110
Lmax : Maximal deformation before break (%) Fig. 13. Maximum deformation before break of the test sample as function of their initial resistivity. Three different horseshoe configurations (h = 0, 30° and 45°) are studied.
5% 10 % 15 % 20 % 25 % 30 %
0.125
Eq. Plastic Strain (-)
3.0
40
Half circle (0º) E=0.7 MPa
0.150
Initial resistivity of the interconnection per unit of lenght (Ohm/cm)
M. Gonzalez et al. / Microelectronics Reliability 48 (2008) 825–832
0.100 0.075
resent the total deformation applied to the structure. These plots show a clear trend: an increase of the scale factor is translated into a reduction of the induced strain. Therefore a narrow copper trace or a large radius of curvature is preferred for these configurations.
0.050 0.025
6. Evaluation of horseshoe design 0.000 0
5
10
15
20
25
Rin / W Horseshoes 45º E=0.7 MPa 0.150 5% 10 % 15 % 20 % 25 % 30 %
Eq. Plastic Strain (-)
0.125 0.100 0.075 0.050 0.025 0.000 0
5
10
15
20
25
Rin / W Fig. 12. Relation between the equivalent plastic strain and the scale factor (R/W) for a substrate with a Young’s Modulus of 0.7 MPa. Top image: semicircle design. Bottom image: Horseshoe design. In both cases, the smaller the scale factor, the higher the plastic strain. A recommended value is between 10 and 15.
of the copper trace and theta (h) is the angle, measured clockwise, where the two arc of circles intersect. When h = 0°, we have a semicircle design, if h > 0°, we obtain the horseshoe design. If we neglect the possible delamination and buckling effects and the relative variation of substrate and metal thickness, it is possible to define a scale factor as the ratio R/W. This means that the stress and strain induced in the metal are constant if the ratio R/W is kept constant, independently of the amplitude of the horseshoe design. A series of 70 models were simulated with different R, W and h in order to find a relation between the damage parameter (plastic strain) and the scale factor R/W. Fig. 12 gives a picture of the relation between plastic strain and the ratio R/W. The different percentages presented in the plots rep-
Based on the FEM results presented above, the induced stresses in the metal under deformation increase drastically if a wide metal track is used. Therefore the single tracks have been made as narrow as the photolithography process allowed it with sufficient reliability, resulting in a width of 15 lm. The spacing between two single tracks is also 15 lm, making the whole ‘‘multitrack” 105 lm wide. On regular points, where the predicted deformation is minimal, neighboring single tracks are connected to each other in order to compensate single track interruptions caused by process faults or mechanical failure. Samples with three different junction angles (h) were fabricated and a tensile test was done. Fig. 13 depicts the maximal deformation of the different samples in relation to its initial resistivity per unit of length. In the case of semicircles design (h = 0o), we obtain the smaller resistivity but also the smaller elongation. Elongations up to 100% and more were obtained in the case of horseshoe design. The large dispersion observed in these results can be explained by the variability of processing parameters, which are not stable enough (silicone thickness uniformity, crystallization of metal during electroplating, presence of defects in the substrate as air bubbles or voids). In all cases, the variation in the resistivity during elongation was below of 2%. 7. Conclusions Several designs of the electrical conductors satisfying the requirements of stretchability were proposed and compared among them by either FEM or experimental tests. From the modeling results, a horseshoe like shape was found to be the optimal; nevertheless, the magnitude of the stresses is related to the stiffness of the substrate and the geometry of the meander. The damage in the metal is significantly reduced by applying narrow metallization schemes and low elastic modulus of the substrate. In order to increase even more the stretchability of the conductors without limiting the electrical performance, four parallel metal conductors of 15 lm width and 15 lm space were fabricated and tested. Based in experimental results, the maximum stretchability achieved with single and wide gold trace was in the order of 20%,
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while for the case of multiple and narrow metallizations the stretchability of the circuits above 100% have been demonstrated. These results show the obvious advantage of using an optimized meander shape and multiple conductor lines in order to allow high deformation of the structure. Acknowledgments The authors would like to thank the Institute for the Promotion of Innovation by Science and Technology in Flanders (IWT) for the financial support through the SBO-Bioflex project (contract number 04101). This work is also supported by European Commission Research program STELLA (Contract Number 028026). www.stella-project.eu. References [1] Spelman F. The past, present, and future of cochlear prostheses. Eng Med Biol Mag IEEE 1999;18(3):27–33.
[2] Clark G. Cochlear implants. Fundamentals and applications. New York: Springer Verlag; 2003. [3] Kudo H et al. A flexible and wearable glucose sensor based on functional polymers with Soft-MEMS techniques. Biosens Bioelectron 2006;22:558–62. [4] Weber J et al. Coin-size coiled-up polymer foil thermoelectric power generator for wearable electronics. Sens Actuators A: Phys 2006;32(1):325–30. [5] Deshpande SD et al. Studies on conducting polymer electroactive paper actuators: effect of humidity and electrode thickness. Smart Mater Struct 2005;14:876–80. [6] Richardson-Burns SM et al. Polymerization of the conducting polymer poly(3,4-ethylenedioxythiophene) (PEDOT) around living neural cells. Biomaterials 2007;28(8):1539–52. [7] Wagner S et al. Electronic skin: architecture and components. Phys E 2004;25:326–34. [8] Lacour SP et al. Stiff subcircuit islands of diamondlike carbon for stretchable electronics. J Appl Phys 2006;100:014913. [9] Sun Z et al. Nat nanotechnol 2006;1:201–7. [10] Gray DS et al. High-conductivity elastomeric electronics. Adv Mater 2004;16(5):393–7. [11] Pelrine R. High-field deformation of elastomeric dielectrics for actuators. Mater Sci Eng C 2000;11:89–100. [12] Brugger J et al. Sens Actuators A: Phys 1998;70(1–2):191–4. [13] Brosteaux D et al., Elastic interconnects for stretchable electronic circuits using mid (moulded interconnect device) technology, In: Proceedings of the MRS spring 2006, vol. 926E.
Contents lists available at ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel
Design of metal interconnects for stretchable electronic circuits Mario Gonzalez a,*, Fabrice Axisa b, Mathieu Vanden Bulcke a, Dominique Brosteaux c, Bart Vandevelde a, Jan Vanfleteren b,c a
IMEC, IPSI/REMO, Kapeldreef 75, 3001 Leuven, Belgium TFCG Microsystems, IMEC, Gent-Zwijnaarde, Belgium c ELIS – TFCG Microsystems, University of Ghent, Gent-Zwijnaarde, Belgium b
a r t i c l e
i n f o
Article history: Received 28 September 2007 Received in revised form 29 January 2008 Available online 5 June 2008
a b s t r a c t The trend of microelectronic products in the textile or medical field is toward higher functionality, miniaturization, application of new materials and a necessity for deformable electronic circuits for improving the comfort control. In this work, the design of flexible and stretchable interconnections is presented. These interconnections are done by embedding sinuous electroplated metallic wires in a stretchable substrate material. A silicone material was chosen as substrate because of its low stiffness and high elongation before break. Common metal conductors used in the electronic industry have very limited elastic ranges; therefore a metallization design is crucial to allow stretchability of the conductors going up to 100%. Different configurations were simulated and compared among them and based on these results, a horseshoe like shape was suggested. This design allows a large deformation with the minimum stress concentration. Moreover, the damage in the metal is significantly reduced by applying narrow metallization schemes. In this way, each conductor track has been split in four parallel lines of 15 lm and 15 lm space in order to improve the mechanical performance without limiting the electrical characteristics. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Flexible and stretchable electronic circuits is a relatively new concept aiming in a first instance at improving the comfort of consumer’s needs. This technology can also be used in many other applications where the ability to deform is an advantage or where the electronics should preferably take the shape of the object in which they are integrated. Some examples of this technology are skin mounted or implantable biomedical devices [1,2] where the circuit must behave as the tissue itself and textile or wearable electronics [3,4]. Traditional signal and power transmission lines in microelectronic systems are placed on rigid or at most flexible substrates, thus limiting the commercial applications to relatively small devices for optimal mobility and comfort. Stretchable electronic circuits will integrate different components onto a compliant polymer substrate that may be stretched once or many times depending on the application. One way to make these circuits is to place rigid or flexible components distributed over a polymer surface and then interconnect these components with a stretchable connection. Nevertheless, one of the critical points in this technology is the reliability of the elastic interconnections. This is particularly challenging given the relatively high and complex * Corresponding author. Tel.: +32 16 28 86 02. E-mail address: [email protected] (M. Gonzalez). 0026-2714/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.microrel.2008.03.025
mechanical loading expected for these applications, i.e. bending, elongation and torsion. Several technologies have been proposed in recent years such as intrinsic conductive polymers [5,6], pre-stressed metal conductors [7–9] or in plane patterned metal conductors [10,11]. Nowadays, metals are the best options to realize these interconnections because of their high electrical performance and relatively low cost. However, in all cases, the main challenge is maintaining the integrity of the circuit during and after flexing or stretching the substrate. In this work, a description of a molded interconnect device (MID) technology is given and the shape of metal interconnections is optimized by finite element analysis (FEA) to allow large deformations. The interconnection between two points will not be a straight line but a periodic undulating metal track. In this way a sort of two-dimensional spring is obtained. As stretchable polymer we use polydimethylsiloxanes (PDMS) because their low elastic modulus and high stretchability. Moreover, PDMS has been used in many medical implantable devices and also in electronics it is not a new material [12]. As a first step, the 3D FEM simulations were used to compare the performance of different shapes (sinus, ‘‘U” shape, half circles, elliptical and ‘‘horseshoe”) and identify the more promising structures that later will be mechanically tested and optimized. The outcome of thermo-mechanical modeling is presented as a stress or strain distribution in the different parts of the structure. The quantification
826
M. Gonzalez et al. / Microelectronics Reliability 48 (2008) 825–832
Fig. 1 outlines the sample fabrication. All processing is done on flexible but non-stretchable substrate which allows using conventional electroplating techniques. In a first instance, a photoresist is spin-coated on a copper foil and patterned, with the meandering shape by UV-radiation. Then a 4 lm thick gold layer was electroplated, followed by a 2 lm nickel layer to improve solderability. Gold was chosen as metal conductor to facilitate the separation of the sacrificial copper foil. However, other metals can be used if an extra thin metal layer is applied on top of the copper foil. Before etching the copper foil, the conductors are encapsulated with 0.25 or 0.5 mm thick elastic polymer. As elastic polymer material Silastic MDX4-4210 from Dow Corning had been chosen because it’s a biomedical grade silicone elastomer with a low Young’s modulus and high elongation (up to 470% from supplier datasheet). More detailed information about this processing was presented by Brosteaux [13].
of an appropriate shape is crucial to allow stretchability of the conductors. For this first approach a 2D plane-stress model was done. The objective of this preliminary study is to compare the stresses induced in a copper conductor when a 20% deformation is applied in the axial direction of the meander. The effect of the substrate was neglected in a first instance. The conductor used for these models is copper with a thickness of 15 lm and a trace width of 90 lm. An amplitude of 700 lm and a period of 500 lm was used for the three proposed configurations (Fig. 2). The mechanical behavior of the copper was modeled as being isotropic, perfect plastic and temperature independent with a Young’s modulus of 117 GPa and an Yield Stress of 172.3 MPa. In a 3D simulation of these configurations an out of plane deformation is observed when a load or displacement is applied in the axial direction (Fig. 3). However, in an actual configuration the metal conductor is embedded into a stretchable substrate and the out of plane deformation is constrained. Therefore, even if a 2D plane stress (in plane deformation) model is not an accurate method because the effects of substrate and metal thickness and the out of plane deformation are not taken into account, it is a good ‘‘first view” of the stresses induced in the structure.
3. Preliminary elastic model
3.1. Deformation analysis of different conductor shapes
Even if simple conductor shapes like triangular or sinusoidal allow higher deformations compared to a straight line, they present a high concentration of stresses in some regions, giving rise to early failures at fairly small deformations. Common metal conductors (Au, Cu, Ni, Pt) have very limited elastic ranges, therefore a design
Three different conductor shapes were analyzed and compared. In all cases, a total deformation of 20% was applied in the axial direction of the meander. Results of these models are presented graphically in Fig. 4. In the case of an elliptical shape (Fig. 4A), a high stress and strain concentration is observed in the crest and trough of the line. In the inner radius, tensile stresses are present, while in the outer radius, compressive stresses are observed. In order to avoid this stress concentration a higher radius of curvature is preferred. The ‘‘U” shape (Fig. 4B) offers a better strain distribution but is still limited by a reduced radius of curvature. Furthermore the straight vertical lines limit the deformation perpendicular to the axis of the meander when a biaxial deformation is needed. In the optimal shape (Fig. 4C); the stress is distributed in an extended part of the conductor. A reduction of 39.2% in the plastic strain is obtained with this shape regarding the elliptical one. As we are just looking for trends, an ‘‘A to B” strain comparison is enough for choosing the conductor shape. Predominant failures are expected in regions where the highest plastic strain concentration is located. Increasing the amplitude of the wave will also reduce the accumulated strain; however, we are limited by the maximum path length allowed for routing. In order to reduce even more the strains in the metal conductor, without sacrificing the electrical performance and/or changing the amplitude or period of the design, the line can be subdivided in several lines of smaller width as shown in Fig. 5. This ‘‘multi-copper trace” improves the stretchability and reduces the induced stresses. In an idealized case (without substrate) for the geometry proposed here, the strains are reduced from 5.25% to only 0.011% if the copper line width is reduced from 90 lm to 10 lm.
of the stresses and strains is based on the substrate stiffness, the width of the metal track and the radius of curvature of these conductors. 2. Sample preparation
Photoresits
Copper Foil 1. Spin coat photoresist 2. Pattern Photoresist
3. Plate metal (Cu, Au, Pt, Ni)
Metal
4. Dissolve Photoresis t
PDMS PDMS 5. Overmould PDMS 6. Etch sacrificial copper foil
7. Invert sample and overmould PDMS Fig. 1. Process sequence for metallic stretchable interconnections embedded in PDMS.
4. FEM simulation of the conductor embedded into the stretchable substrate In order to quantify the strains in the copper meander, the substrate has to be included. When the substrate is stretched in the axial direction, due to the Poisson’s effect, the tensile deformation is always accompanied by a lateral contraction as shown in Fig. 6. During a uniaxial stretching, global and local deformations are observed. Globally, the copper conductor is under tension when the line is parallel to the stretching direction and is under compression
M. Gonzalez et al. / Microelectronics Reliability 48 (2008) 825–832
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Fig. 2. Different conductor shapes for metallic stretchable interconnections embedded in a stretchable matrix.
Fig. 3. Out of plane deformation of an unconstrained copper meander stretched 20%.
when the copper trace is perpendicular to the stretching direction. Locally, the inner part of the copper trace is in tension and the outer part in compression. The magnitude of the strains caused by the local or global deformation depends on the stiffness of the substrate and the thickness of the copper trace. The dashed line in Figs. 6 and 7 indicate the original dimensions of the structure. From these images it is seen that the accumulated plastic strain for the
multi-track design is more than six times smaller than the original single track design. We have to underline that the conductor shape is optimized for a uniaxial deformation in the direction of the conductor. Other complex deformation such as biaxial and torsion are under investigation. A qualitative comparison between modeling and experiments shows that calculated regions with high concentration of plastic
828
M. Gonzalez et al. / Microelectronics Reliability 48 (2008) 825–832
Fig. 4. Plastic strain distribution in copper conductor line for three different conductor shapes. (A) Elliptical shape; (B) ‘‘U” shape; (C) horseshoe shape.
strain ðepl max ffi 10%Þ correspond to the observed failures (Fig. 8). Visible cracks are observed in the crests and troughs of the meander at about 25% of total deformation. Because the copper conductor is completely embedded into the stretchable matrix, 2D plane stress or plane strain models cannot
be used. Those models assume a unique material in the thickness direction. For solving this problem 3D FEM has to be used. However, 3D models require high number of memory and computational time. The same 3D effect can be obtained by using composite shell elements. Those elements are composed of layers
M. Gonzalez et al. / Microelectronics Reliability 48 (2008) 825–832
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Fig. 5. Plastic strain distribution in a multi-track horseshoe conductor design.
Fig. 6. Poisson effect observed during a uniaxial tension test for a single conductor line. Dashed line shows the original dimensions of the substrate.
of different materials with various layer thicknesses. Furthermore, the material in each layer may be linear or not linear. Therefore, gold or copper can be modeled as a perfect plastic material. In order to validate the accuracy of the 2D composite elements, a horseshoe meander was modeled by using 3D brick elements and 2D composite shell elements. In both cases, the PDMS material was modeled as a hyperelastic material. A Neo-Hooke model (C10 = 0.157 MPa) gives an acceptable fit for nominal strain levels up to 100%. Results of this comparison are depicted in Fig. 9. The continuous line shows the strains calculated with the 3D model and the points represent the plastic strain calculated in the copper meander by using composite 2D elements. As the difference between 2D and 3D elements is negligible and calculation time was divided by 10 it is advisable to use 2D composite shell elements to model these structures. The deformation of the patterned metal conductor is, in a certain manner, controlled by the deformation of the stretchable substrate. If the conductor is embedded in a stiff substrate, the deformation of the conductor will be the same as the one of the substrate. On the other hand, if a very soft substrate is used, the conductor has some ‘‘freedom” to move inside the substrate,
reducing in this way the Poisson’s effect and in consequence, the accumulated plastic strain (compressive stresses are reduced). To quantify the maximum strain in the conductor as a function of the stiffness of the substrate, the meander design presented in Fig. 6 was modeled with different Young’s modulus of the substrate. For this comparative study the substrate is modeled as a linear elastic material with a Young’s modulus varying from 5 to 150 MPa. In this case, the thickness of copper and substrate were kept constant with values of 17 lm and 100 lm respectively. Results of this study are presented in Fig. 10. For this configuration, when the Young’s Modulus of the substrate is about 120 MPa, the plastic strain in the copper is practically the same as the total strain applied to the substrate. This means, that increasing the stiffness of the substrate will decrease the maximum allowable stretchability of the structure without electrical failure.
5. Parameters used in the horseshoe design The horseshoe pattern is created by joining a series of circular arcs as shown in Fig. 11, where R is the inner radius, W is the width
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Fig. 7. Poisson effect observed during a uniaxial tension test for a multiple conductor line. Dashed line shows the original dimensions of the substrate.
Fig. 8. Tensile strain test of horseshoe metal interconnects embedded into a Sylgard 186 PDMS matrix. (a) Before elongation, (b) After 25% elongation highlighting the failures in the crest and trough.
14
zone 2
10
20
Max. Eq. Plastic Strain (%)
Eq. Plastic Strain (-)
Zone 1 - 3D Zone 2 - 3D Zone 1 - 2D Zone 2 - 2D
zone 1
12
8 6 4 2
15
10 t Cu = 17 µm t subs = 100 µm Total deformation = 20%
5
0 0
5
10
15
20
25
30
Total deformation (%)
0 0
20
40
60
80
100
120
140
160
Young's Modulus of Substrate (MPa) Fig. 9. Comparison of the equivalent plastic strain induced in the copper conductor embedded into a PDMS matrix as function of the applied deformation. Thickness of copper: 17 lm; thickness of PDMS: 100 lm.
Fig. 10. Equivalent plastic strain induced in the copper as function of the Young’s Modulus of the substrate.
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R θ
θ=0º
w
θ=45º Fig. 11. Definition of horseshoe design by its inner radius (R), joining angle (h) and width of the metal track (w).
2.5 2.0 1.5 1.0
Θ =0 Θ=30
0.5
Θ=45
0.0 50
60
70
80
90
100
110
Lmax : Maximal deformation before break (%) Fig. 13. Maximum deformation before break of the test sample as function of their initial resistivity. Three different horseshoe configurations (h = 0, 30° and 45°) are studied.
5% 10 % 15 % 20 % 25 % 30 %
0.125
Eq. Plastic Strain (-)
3.0
40
Half circle (0º) E=0.7 MPa
0.150
Initial resistivity of the interconnection per unit of lenght (Ohm/cm)
M. Gonzalez et al. / Microelectronics Reliability 48 (2008) 825–832
0.100 0.075
resent the total deformation applied to the structure. These plots show a clear trend: an increase of the scale factor is translated into a reduction of the induced strain. Therefore a narrow copper trace or a large radius of curvature is preferred for these configurations.
0.050 0.025
6. Evaluation of horseshoe design 0.000 0
5
10
15
20
25
Rin / W Horseshoes 45º E=0.7 MPa 0.150 5% 10 % 15 % 20 % 25 % 30 %
Eq. Plastic Strain (-)
0.125 0.100 0.075 0.050 0.025 0.000 0
5
10
15
20
25
Rin / W Fig. 12. Relation between the equivalent plastic strain and the scale factor (R/W) for a substrate with a Young’s Modulus of 0.7 MPa. Top image: semicircle design. Bottom image: Horseshoe design. In both cases, the smaller the scale factor, the higher the plastic strain. A recommended value is between 10 and 15.
of the copper trace and theta (h) is the angle, measured clockwise, where the two arc of circles intersect. When h = 0°, we have a semicircle design, if h > 0°, we obtain the horseshoe design. If we neglect the possible delamination and buckling effects and the relative variation of substrate and metal thickness, it is possible to define a scale factor as the ratio R/W. This means that the stress and strain induced in the metal are constant if the ratio R/W is kept constant, independently of the amplitude of the horseshoe design. A series of 70 models were simulated with different R, W and h in order to find a relation between the damage parameter (plastic strain) and the scale factor R/W. Fig. 12 gives a picture of the relation between plastic strain and the ratio R/W. The different percentages presented in the plots rep-
Based on the FEM results presented above, the induced stresses in the metal under deformation increase drastically if a wide metal track is used. Therefore the single tracks have been made as narrow as the photolithography process allowed it with sufficient reliability, resulting in a width of 15 lm. The spacing between two single tracks is also 15 lm, making the whole ‘‘multitrack” 105 lm wide. On regular points, where the predicted deformation is minimal, neighboring single tracks are connected to each other in order to compensate single track interruptions caused by process faults or mechanical failure. Samples with three different junction angles (h) were fabricated and a tensile test was done. Fig. 13 depicts the maximal deformation of the different samples in relation to its initial resistivity per unit of length. In the case of semicircles design (h = 0o), we obtain the smaller resistivity but also the smaller elongation. Elongations up to 100% and more were obtained in the case of horseshoe design. The large dispersion observed in these results can be explained by the variability of processing parameters, which are not stable enough (silicone thickness uniformity, crystallization of metal during electroplating, presence of defects in the substrate as air bubbles or voids). In all cases, the variation in the resistivity during elongation was below of 2%. 7. Conclusions Several designs of the electrical conductors satisfying the requirements of stretchability were proposed and compared among them by either FEM or experimental tests. From the modeling results, a horseshoe like shape was found to be the optimal; nevertheless, the magnitude of the stresses is related to the stiffness of the substrate and the geometry of the meander. The damage in the metal is significantly reduced by applying narrow metallization schemes and low elastic modulus of the substrate. In order to increase even more the stretchability of the conductors without limiting the electrical performance, four parallel metal conductors of 15 lm width and 15 lm space were fabricated and tested. Based in experimental results, the maximum stretchability achieved with single and wide gold trace was in the order of 20%,
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while for the case of multiple and narrow metallizations the stretchability of the circuits above 100% have been demonstrated. These results show the obvious advantage of using an optimized meander shape and multiple conductor lines in order to allow high deformation of the structure. Acknowledgments The authors would like to thank the Institute for the Promotion of Innovation by Science and Technology in Flanders (IWT) for the financial support through the SBO-Bioflex project (contract number 04101). This work is also supported by European Commission Research program STELLA (Contract Number 028026). www.stella-project.eu. References [1] Spelman F. The past, present, and future of cochlear prostheses. Eng Med Biol Mag IEEE 1999;18(3):27–33.
[2] Clark G. Cochlear implants. Fundamentals and applications. New York: Springer Verlag; 2003. [3] Kudo H et al. A flexible and wearable glucose sensor based on functional polymers with Soft-MEMS techniques. Biosens Bioelectron 2006;22:558–62. [4] Weber J et al. Coin-size coiled-up polymer foil thermoelectric power generator for wearable electronics. Sens Actuators A: Phys 2006;32(1):325–30. [5] Deshpande SD et al. Studies on conducting polymer electroactive paper actuators: effect of humidity and electrode thickness. Smart Mater Struct 2005;14:876–80. [6] Richardson-Burns SM et al. Polymerization of the conducting polymer poly(3,4-ethylenedioxythiophene) (PEDOT) around living neural cells. Biomaterials 2007;28(8):1539–52. [7] Wagner S et al. Electronic skin: architecture and components. Phys E 2004;25:326–34. [8] Lacour SP et al. Stiff subcircuit islands of diamondlike carbon for stretchable electronics. J Appl Phys 2006;100:014913. [9] Sun Z et al. Nat nanotechnol 2006;1:201–7. [10] Gray DS et al. High-conductivity elastomeric electronics. Adv Mater 2004;16(5):393–7. [11] Pelrine R. High-field deformation of elastomeric dielectrics for actuators. Mater Sci Eng C 2000;11:89–100. [12] Brugger J et al. Sens Actuators A: Phys 1998;70(1–2):191–4. [13] Brosteaux D et al., Elastic interconnects for stretchable electronic circuits using mid (moulded interconnect device) technology, In: Proceedings of the MRS spring 2006, vol. 926E.
