APPLIED PHYSICS LETTERS 90, 214103 共2007兲
Powerful polymeric thermal microactuator with embedded silicon microstructure G. K. Lau,a兲 J. F. L. Goosen, and F. van Keulen Department of Precision and Microsystems Engineering, Faculty of 3ME, Delft University of Technology, Delft 2628 CD, The Netherlands
T. Chu Duc and P. M. Sarro Laboratory of Electronic Components, Technology and Materials, DIMES, Delft University of Technology, Delft 2600 GB, The Netherlands
共Received 13 March 2007; accepted 1 May 2007; published online 23 May 2007兲 A powerful and effective design of a polymeric thermal microactuator is presented. The design has SU-8 epoxy layers filled and bonded in a meandering silicon 共Si兲 microstructure. The silicon microstructure reinforces the SU-8 layers by lateral restraint. It also improves the transverse thermal expansion coefficient and heat transfer for the bonded SU-8 layers. A theoretical model shows that the proposed SU-8/Si composite can deliver an actuation stress of 1.30 MPa/ K, which is approximately 2.7 times higher than the unconstrained SU-8 layer, while delivering an approximately equal thermal strain. © 2007 American Institute of Physics. 关DOI: 10.1063/1.2742599兴 Thermal actuators feature relatively high actuation stress or strain. However, they have shortcomings in terms of high power consumption and high operating temperatures.1,2 To a large extent, their performance depends on the selected thermal expansion materials.3 For example, silicon and metals with high moduli of elasticity produce high actuation stresses, but polymers with high thermal expansion coefficients 共CTEs兲 deliver relatively high actuation strains. According to Ashby,4 the linear CTE 共␣兲 is almost inversely proportional to Young’s modulus 共E兲. This means that compliant but high-CTE polymers may not be ideal for generating large actuation stress and strain simultaneously. Owing to their electrical and thermal insulating properties, most polymers require integrated heaters to enable electrical activation.2,5 The heaters are normally made of surface metallic films and may induce nonuniform heating across the polymeric thickness. This may inevitably cause out-of-plane bending to the polymeric layers. In this letter, we present a design of polymeric thermal actuators to accomplish enhanced in-plane actuation. This design combines multiple materials for effective thermal actuation. It consists of an aluminum film heater, a silicon 共Si兲 microstructure, and polymeric epoxy 共SU-8兲 encapsulant 共see Fig. 1兲. The silicon microstructure is meandering in shape and has a high aspect ratio. Its gaps and surrounding areas are filled and encapsulated with SU-8 epoxy, whereas its top is covered with the aluminum 共Al兲 heater. The Si “skeleton” serves to conduct heat and to reinforce the SU-8 encapsulant; the Al line is responsible for resistive heating; whereas, the SU-8 epoxy serves to expand and open the spacing of the Si skeleton. The proposed design has been fabricated using bulk micromachining of silicon and casting of SU-8-2002 polymer.6 Testing shows that a 530-m-long sample device 共consisting of a 0.675-m-thick Al film and a 50-m-high Si microstrcutrure兲 delivers a 2.5% in-plane longitudinal strain at 2 V, while consuming less than 27 mW 关see Fig. 1共b兲兴, and shows a兲
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no noticeable out-of-plane motion. The actuation using this composite design is efficient. This motivates investigation into its potential actuation capabilities. The normal activation of the actuator design by resistive heating causes an unknown and nonuniform temperature distribution. This may obscure the influences of thermoelastic properties on the actuation capability. Therefore, external uniform heating is adopted in the theoretical and experimental evaluations below to exclude this effect and accurately control the temperature. The confined SU-8 filling in the meandering silicon microstructure is similar in configuration to a polymeric layer sandwiched between two silicon layers in a composite stack 关see Fig. 1共a兲兴. The silicon layers reinforce the polymeric layer by the lateral restraint on the bond interface. As a result, the volumetric expansion of the polymer layer is con-
FIG. 1. 共a兲 Schematic drawing of the proposed polymeric thermal actuator, consisting of a symmetrically meandering silicon 共Si兲 microstructure, SU-8 encapsulant, and an aluminum 共Al兲 heater, together with a representative unit cell of three layers 共Si/SU-8/Si兲. 共b兲 The measured tip displacement for a sample device 共h = 50 m, tc = 3 m, and t p = 3 m, and w = 28 m兲 as a function of input power when electrically activated by the aluminum heater 共0.675 m thick兲.
0003-6951/2007/90共21兲/214103/3/$23.00 90, 214103-1 © 2007 American Institute of Physics Downloaded 10 Aug 2010 to 131.180.130.114. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
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Appl. Phys. Lett. 90, 214103 共2007兲
Lau et al. TABLE I. Comparison of thermal expandable materials.
Young’s modulus 共E兲 共GPa兲 Poisson’s ratio 共兲 Linear CTE 共␣兲 共⫻10−6 / K兲 Thermal conductivity 共W/m K兲 Maximum temperature 共°C兲 Actuation stress 共E ⫻ ␣兲 共MPa/K兲 Energy density 关共1 / 2兲E ⫻ ␣2兴 共J / m3 K2兲
Ala
Sib
SU-8c
50/ 50%d SU-8/Si composite
69 0.35 23.1 237 660 共Tm兲 1.59 18.41
130 0.28 2.6 148 1414 共Tm兲 0.35 0.48
3.2 0.33 150.7 0.2 238 共Tg兲 0.48 36.32
8.89⬜ ¯ 146.2⬜ 0.4⬜ / 74.1储 238 1.30⬜ 95.04⬜
a
Reference 12. References 12 and 13. c References 10 and 11. d Based on Eqs. 共1兲–共4兲 derived from the three-layered model. b
centrated perpendicular to the bond interface, with little lateral bulging at the free edges. The phenomenon of directionally enhanced thermal strain was observed as an unintended effect in a stacked memory cube with adhesive layers.7 In this work, we exploit the effect for enhancing electrothermal actuation. A laminar model is developed to evaluate performance of a representative unit cell, which consists of three infinitely wide layers 共Si/SU-8/Si兲. The material properties are assumed linear and isotropic,8 well below the polymeric glass transition temperature 共Tg兲 or below the silicon melting temperature 共Tm兲. Flexibility coupling between the bonded polymer and silicon layers is considered in the constitutive equations, 1 + p p p p − ␦ij + ␣ p⌬T␦ij E p ij E p kk
eijp =
1 + c c c c and ecij = − ␦ij + ␣c⌬T␦ij , Ec ij Ec kk
1 共1兲
where eij is the strain tensor; ij is the stress tensor, and ␦ij is the Kronecker delta. Summation convention is used for repeated indices.9 Referring to Fig. 1共a兲, indices 11 and 22 denote the lateral directions 共储兲 parallel to the layer sidewalls, whereas index 33 denotes the transverse direction 共⬜兲. Both the lateral and transverse directions are parallel to the wafer plane. The superscripts p and c denote polymeric and conductive silicon layers, respectively. The symbols E and denote Young’s moduli and Poisson’s ratio, respectively. In each layer, transverse thermal strains are assumed uniform under a uniform temperature rise ⌬T and zero external loading. Lateral strains are common at the interface between the layers. The lateral force summation is zero, but the internal lateral stresses in the layers are nonzero due to the CTE mismatch. In the transverse direction, the apparent CTE for the constrained polymer layer increases, but that for the silicon layers decreases. The transverse CTEs for the bonded layers are derived below, in which ␥ = t pE p / 2tcEc: p ␣⬜ =
p e33 2 p共 ␣ p − ␣ c兲 = ␣p + ⌬T 1 − p + ␥共1 − c兲 c = and ␣⬜
c e33 2 c共 ␣ p − ␣ c兲 = ␣c − . ⌬T 共1 − c兲 + ␥−1共1 − p兲
c p in Eq. 共2兲: ␣⬜ = 共1 − 兲␣⬜ + ␣⬜ , in which = t p / 共t p + 2tc兲 is the volume fraction of the polymer component. In the limiting case where ␥ = 0, ␣c = 0, the apparent polymeric CTE becomes ␣ p共1 + 兲 / 共1 − 兲. Owing to the lateral restraint of the stiff silicon layers, the bonded polymer layer undergoes less transverse strain when loaded transversely. The enhanced stiffness is derived by solving Eq. 共1兲 with ⌬T = 0 and nonzero transverse p c = 33 ⫽ 0, and using the same assumptions of latstresses 33 eral force equilibrium and displacement compatibility as above. The apparent transverse modulus 共E⬜兲 for the com−1 c −1 p −1 posite stack is derived as: E⬜ = 共1 − 兲共E⬜ 兲 + 共E⬜ 兲 , in p which Young’s modulus for the constrained polymer 共E⬜ 兲 c and that for the constrained conductors 共E⬜兲 are given below, together with = E p / Ec
共2兲
The apparent transverse thermal expansion coefficient of the three-layer model is a sum of the component coefficients
p E⬜
=
p e33 p 33
and
=
冋
1 2 p共 p − c兲 p 1− E 1 − p + ␥共1 − c兲
1 c E⬜
=
c e33 c 33
=
冋
册
册
1 2␥c共 p − c兲 1 + . Ec 1 − p + ␥共1 − c兲
共3兲
Furthermore, the embedded silicon microstructructure improves heat transfer to the insulating polymers. The transverse thermal conductivity 共k⬜兲 and the lateral 共k储兲 for the polymeric composite stack are derived below, 1 1 1 = + 共1 − 兲 k1 k⬜ k2
and k储 = k1 + 共1 − 兲k2 .
共4兲
Table I compares the derived properties for the 50/ 50% Si/SU-8 composite design 共i.e., at = 0.5兲 with those for the base materials, such as silicon, epoxy, and aluminum.10–13 It is shown that the composite design has tremendous improvement in the actuation capability. The constrained CTE for SU-8 epoxy is estimated to double, resulting in an apparent composite CTE equal to the unconstrained SU-8 CTE. In addition, the composite produces more than double the actuation stress per kelvin 共E⬜ ⫻ ␣⬜兲 as compared to those of silicon or epoxy. The actuation stress at ⌬T ⬎ 10 ° C easily exceeds those generated by electroactive polymers at several kilovolts.14,15 Furthermore, the actuation energy density per 2 兴 is more than four times squared kelvin 关共1 / 2兲E⬜ ⫻ ␣⬜ higher than that of aluminum, which is known for its high CTE among metals.16 The transverse thermal conductivity doubles, and the lateral conductivity becomes even better,
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Appl. Phys. Lett. 90, 214103 共2007兲
Lau et al.
FIG. 2. Microscope images showing full and partial views of the micromachined devices: 共a兲 a scanning electron micrograph of a sample device still residing on silicon substrate 共h = 50 m, tc = 3 m, and t p = 3 m兲; 共b兲 An optical image of a polymeric actuator with 53 m wide 共w兲 meandering silicon microstructure; 共c兲 an optical image of a polymeric actuator with 103 m wide 共w兲 parallel plates.
reaching a half of the silicon conductivity. Hence, heat transfer across the thick polymer layers in the composite is greatly enhanced. In the present composite design, the constituent polymer is fully constrained in the high-aspect-ratio meandering microstructure. Therefore, the bonded polymeric layers exhibit bulk properties. Without the constraint, a free SU-8 layer, expanding in all directions, does not deliver as much concentrated work as the constrained layer does. A bulk SU-8 sample under hydrostatic compression is reported to have higher Young’s modulus and CTE than a planar film sample under directional strectching. For example, the bulk has a volumetric CTE of 452 ppm/ K, while the linear in-plane CTE of the thin film ranges between 87 and 102 ppm/ K.10,11 Moreover, the bulk modulus is 5.88 GPa, while the thin-film in-plane modulus is 3.2 GPa.10,11 This polymeric composite design well exploits the bulk SU-8 properties by layered confinement for unidirectional actuation. To measure the apparent transverse CTE of the composite, a 4 in. wafer with released micromachined composite actuators is placed on a temperature controllable hot plate. It is heated up to the desired steady-state temperature, which is measured with a thermocouple. In-plane dimension changes, i.e., ⌬L / L, of the devices are measured by comparing the focused images at an elevated temperature 共155± 5 ° C兲 with those at the room temperature 共25° C兲. Figure 2 shows examples of optical microscope images 共model: Keyence VHX兲. Figure 3 shows that the transverse dimensional change increases with the width of the silicon meandering microstructures. This is attributed partly to the enhancement in constrained thermal expansion and partly to the reduced influence of the horseshoe bends of the meandering silicon microstructures. The measured CTE agrees in trend with that simulated using a three-dimensional finite element 共FE兲 model. The FE analysis is performed using ANSYS. At a large layer width, the simulated and measured CTEs approach to an asymptotic value predicted by the laminar model. The measured CTE reaches 140 ppm/ ° C at a 103 m layer width. In addition, the FE and laminar models predict that
FIG. 3. Trends of the apparent transverse CTE 共top兲 and the blocked transverse stress 共bottom兲 with respect to the aspect ratio of the layer width to the spacing between the layers, for two polymeric composite designs: 共i兲 embedded with parallel silicon plates or 共ii兲 embedded with meandering silicon microstructures.
the blocked transverse actuation stress for the composite stack exceeds that of unconstrained SU-8. In summary, a polymeric composite design of thermal actuators demonstrated enhanced in-plane actuation. The composite actuator 共50/ 50% SU-8/Si兲 outperforms the homogenous materials, in terms of thermal stress-strain generation and energy density. This actuator design, which embeds a high-aspect-ratio silicon microstructure, could be extended to various expandable polymers, both thermally and chemically driven, for effective in-plane actuation. The authors acknowledge DIMES for support in device fabrication, the Delft Center of Mechatronics and Microsystems 共DCMM兲, and the Dutch MicroNed programme for financial support. 1
L. Que, J. S. Park, and Y. B. Gianchandani, J. Microelectromech. Syst. 10, 247 共2001兲. 2 M. Ataka, A. Omodaka, N. Takeshima, and H. Fujita, J. Microelectromech. Syst. 2, 146 共1993兲. 3 J. E. Huber, N. A. Fleck, and M. F. Ashby, Proc. R. Soc. London, Ser. A 453, 2185 共1997兲. 4 M. F. Ashby, Acta Metall. 37, 1273 共1989兲. 5 N. T. Nguyen, S. S. Ho, and C. L. N. Low, J. Micromech. Microeng. 14, 969 共2004兲. 6 G. K. Lau, J. F. L. Goosen, F. van Keulen, T. Chu Duc, and P. M. Sarro, Proceedings of the 5th IEEE Conference on Sensors, Daegu, Korea, 22–26 October 2006 共IEEE, New York, 2007兲, pp. 538–541. 7 B. Han and Y. Guo, IEEE Trans. Compon., Packag., Manuf. Technol., Part C 19, 240 共1996兲. 8 T. Y. Wu, Y. Guo, and W. T. Chen, IBM J. Res. Dev. 37, 621 共1993兲. 9 M. H. Sadd, Elasticity: Theory, Applications, and Numerics 共Elsevier Butterworth-Heinemann, Amsterdam, 2004兲, pp. 77, 78. 10 R. Feng and J. Farris, J. Mater. Sci. 37, 4793 共2002兲. 11 R. Feng and J. Farris, J. Micromech. Microeng. 13, 80 共2003兲. 12 CRC Handbook of Chemistry and Physics, Internet Version 2007, 87th ed., edited by D. R. Lide 共Taylor and Francis, Boca Raton, FL, 2007兲, Sec. 12, pp. 35, 77, 219, http:/www.hbcpnetbase.com. 13 J. J. Wortman and R. A. Evans, J. Appl. Phys. 36, 153 共1965兲. 14 Q. M. Zhang, V. Bharti, and X. Zhao, Science 280, 2101 共1998兲. 15 R. Pelrine, R. Kornbluh, Q. Pei, and J. Joseph, Science 287, 836 共2000兲. 16 B. Z. Jang and Z. J. Zhang, J. Intell. Mater. Syst. Struct. 5, 758 共1994兲.
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