0
Journal of Heat Transfer | Volume 134 | Issue 11 | Micro/Nanoscale Heat Transfer
Research Papers: Micro/Nanoscale Heat Transfer

Thermal Actuation Using Nanocomposites: A Computational Analysis

Y. Xu and G. Li
[+] Author and Article Information
Y. Xu

 Department of Mechanical Engineering, Clemson University, Clemson, SC 29634

G. Li1

 Department of Mechanical Engineering, Clemson University, Clemson, SC 29634gli@clemson.edu

1

Corresponding author.

J. Heat Transfer 134(11), 112401 (Sep 28, 2012) (11 pages) doi:10.1115/1.4007128 History: Received April 04, 2011; Revised June 04, 2012; Published September 26, 2012; Online September 28, 2012
Article
References
Figures
Tables

In this paper, we propose the use of Si/Ge nanocomposite materials to improve the performance of microthermal actuators. Nanocomposites with a high electrical to thermal conductivity ratio can facilitate a rapid temperature change within a short distance, enabling a high temperature increase in a large region of the actuator beams. The total structural thermal expansion and, consequently, the actuation distance can be increased significantly. A top-down quasi-continuum multiscale model is presented for the computational analysis of nanocomposite based thermal actuators. In the multiscale model, the thermo-mechanical response of the actuator due to Joule heating is modeled using classical continuum theories, while the thermal and electrical properties of doped Si and Si/Ge nanocomposite materials are obtained from atomistic level descriptions. An iterative procedure is carried out between the calculations at the two length scales until a self-consistent solution is obtained. Numerical results indicate that incorporating Si/Ge nanocomposites in thermal actuators can significantly increase their energy efficiency and mechanical performance. In addition, parametric studies show that the size of the nanocomposite region and atomic percentage of the material components have significant effects on the overall performance of the actuators.
Copyright © 2012 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

1
Comtois, J. H., and Bright, V. M., 1997, “Applications for Surface-Micromachined Polysilicon Thermal Actuators and Arrays,” Sens. Actuators, A, 58 , pp. 19–25.  [CrossRef]
2
Que, L., Park, J.-S., and Gianchandani, Y. B., 2001, “Bent-Beam Electrothermal Actuators—Part I: Single Beam and Cascaded Devices,” J. Microelectromech. Syst., 10 (2), pp. 247–254.  [CrossRef]
3
Huang, Q.-A., and Lee, N. K. S., 1999, “Analysis and Design of Polysilicon Thermal Flexure Actuator,” J. Micromech. Microeng., 9 (1), pp. 64–70.  [CrossRef]
4
Hickey, R., Kujath, M., and Hubbard, T., 2002, “Heat Transfer Analysis and Optimization of Two-Beam Microelectromechanical Thermal Actuators,” J. Vac. Sci. Technol. A, 20 , pp. 971–974.  [CrossRef]
5
Sigmund, O., 2001, “Design of Multiphysics Actuators Using Topology Optimization,”Comput. Methods Appl. Mech. Eng., 190 , pp. 6577–6627.  [CrossRef]
6
Yan, D., Khajepour, A., and Mansour, R., 2004, “Design and Modeling of a MEMS Bidirectional Vertical Thermal Actuator,” J. Micromech. Microeng., 14 (7), pp. 841–850.  [CrossRef]
7
Chen, S. C., and Culpepper, M. L., 2006, “Design of Contoured Microscale Thermomechanical Actuators,” J. Microelectromech. Syst., 15 (5), pp. 1226–1234.  [CrossRef]
8
Sassen, W. P., Henneken, V. A., Tichem, M., and Sarro, P. M., 2008, “Contoured Thermal V-Beam Actuator With Improved Temperature Uniformity,” Sens. Actuators, A, 144 (2), pp. 341–347.  [CrossRef]
9
Joshi, A. A., and Majumdar, A., 1993, “Transient Ballistic and Diffusive Phonon Heat Transport in Thin Films,” J. Appl.Phys., 74 (1), pp. 31–39.  [CrossRef]
10
Chen, G., 1998, “Thermal Conductivity and Ballistic-Phonon Transport in the Cross-Plane Direction of Superlattices,” Phys. Rev. B, 57 (23), pp. 14958–14973.  [CrossRef]
11
Yang, R., and Chen, G., 2004, “Thermal Conductivity Modeling of Periodic Two-Dimensional Nanocomposites,” Phys. Rev. B, 69 , p. 195316.  [CrossRef]
12
Minnich, A. J., Lee, H., Wang, X. W., Joshi, G., Dresselhaus, M. S., Ren, Z. F., Chen, G., and Vashaee, D., 2009, “Modeling Study of Thermoelectric SiGe Nanocomposites,” Phys. Rev. B, 80 (15), p. 155327.  [CrossRef]
13
Xie, W., He, J., Kang, H. J., Tang, X., Zhu, S., Laver, M., Wang, S., Copley, J. R. D., Brown, C. M., Zhang, Q., and Tritt, T. M., 2010, “Identifying the Specific Nanostructures Responsible for the High Thermoelectric Performance of (Bi,Sb)2 Te3 Nanocomposites,” Nano Lett., 10 (9), pp. 3283–3289.  [CrossRef]
14
Mankame, N. D., and Ananthasuresh, G. K., 2001, “Comprehensive Thermal Modelling and Characterization of an Electro-Thermal-Compliant Microactuator,” J. Micromech. Microeng., 11 (5), p. 452–462.  [CrossRef]
15
Zhao, H., Tang, Z., Li, G., and Aluru, N. R., 2006, “Quasiharmonic Models for the Calculation of Thermodynamic Properties of Crystalline Silicon Under Strain,” J. Appl.Phys., 99 (6), p. 064314.  [CrossRef]
16
Tang, Z., Zhao, H., Li, G., and Aluru, N. R., 2006, “Finite-Temperature Quasicontinuum Method for Multiscale Analysis of Silicon Nanostructures,” Phys. Rev. B, 74 (6), p. 064110.  [CrossRef]
17
Guckel, H., Klein, J., Christenson, T., Skrobis, K., Laudon, M., and Lovell, E. G., 1992, “Thermo-Magnetic Metal Flexure Actuators,” "5th Technical Digest", IEEE Solid-State Sensor and Actuator Workshop, pp. 73–75.
18
Minnich, A. J., Dresselhaus, M. S., Ren, Z. F., and Chen, G., 2009, “Bulk Nanostructured Thermoelectric Materials: Current Research and Future Prospects,” Energy Environ.Sci, 2 (5), pp. 466–479.  [CrossRef]
19
Wang, X. W., Lee, H., Lan, Y. C., Zhu, G. H., Joshi, G., Wang, D. Z., Yang, J., Muto, A. J., Tang, M. Y., Klatsky, J., Song, S., Dresselhaus, M. S., Chen, G., and Ren, Z. F., 2008, “Enhanced Thermoelectric Figure of Merit in Nanostructured n-Type Silicon Germanium Bulk Alloy,” Appl. Phys. Lett., 93 , p. 193121.  [CrossRef]
20
Dresselhaus, M. S., Chen, G., Tang, M. Y., Yang, R., Lee, H., Wang, D., Ren, Z., Fleurial, J.-P., and Gogna, P., 2007, “New Directions for Low-Dimensional Thermoelectric Materials,” Adv. Maters, 19 (8), pp. 1043–1053.  [CrossRef]
21
Sniegowski, J. J., and de Boer, M. P., 2000, “IC-Compatible Polysilicon Surface Micromachining,” Ann. Rev. Mater. Sci., 30 , pp. 299–333.  [CrossRef]
22
Hashin, Z., and Shtrikman, S., 1963, “A Variational Approach to the Theory of the Elastic Behaviour of Multiphase Materials,” J. Mech. Phys. Solids, 11 (2), pp. 127–140.  [CrossRef]
23
Hill, R., 1965, “Theory of Mechanical Properties of Fibre-Strengthened Materials—III: Self-Consistent Model,” J. Mech. Phys. Solids, 13 (4), pp. 189–198.  [CrossRef]
24
Walpole, L. J., 1969, “On the Overall Elastic Moduli of Composite Materials,” J. Mech. Phys. Solids, 17 (4), pp. 235–251.  [CrossRef]
25
Mori, T., and Tanaka, K., 1973, “Average Stress in Matrix and Average Elastic Energy of Materials With Misfitting Inclusions,” Acta Metall., 21 (5), pp. 571–574.  [CrossRef]
26
Chen, T., Dvorak, G. J., and Benveniste, Y., 1992, “Mori-Tanaka Estimates of the Overall Elastic Moduli of Certain Composite Materials,” ASME J. Appl. Mech., 59 (3), pp. 539–546.  [CrossRef]
27
Benveniste, Y., Dvorak, G. J., and Chen, T., 1991, “On Diagonal and Elastic Symmetry of the Approximate Effective Stiffness Tensor of Heterogeneous Media,” J. Mech. Phys. Solids, 39 (7), pp. 927–946.  [CrossRef]
28
Dvorak, G. J., and Benveniste, Y., 1992, “On Transformation Strains and Uniform Fields in Multiphase Elastic Media,” Proc. R. Soc. London, Ser. A, 437 (1900), pp. 291–310.  [CrossRef]
29
Reiter, T., Dvorak, G. J., and Tvergaard, V., 1997, “Micromechanical Models for Graded Composite Materials,” J. Mech. Phys. Solids, 45 (8), pp. 1281–1302.  [CrossRef]
30
Hill, R., 1964, “Theory of Mechanical Properties of Fibre-Strengthened Materials: I. Elastic Behaviour,” J. Mech. Phys. Solids, 12 (4), pp. 199–212.  [CrossRef]
31
Wortman, J. J., and Evans, R. A., 1965, “Young’s Modulus, Shear Modulus, and Poisson’s Ratio in Silicon and Germanium,” J. Appl. Phys., 36 , pp. 153–156.  [CrossRef]
32
Ono, N., Kitamura, K., Nakajima, K., and Shimanuki, Y., 2000, “Measurement of Young’s Modulus of Silicon Single Crystal at High Temperature and Its Dependency on Boron Concentration Using the Flexural Vibration Method,” Jpn. J. Appl. Phys., Part 1, 39 (2A), pp. 368–371.  [CrossRef]
33
Gladden, J. R., Li, G., Adebisi, R., Firdosy, S., Caillat, T., and Ravi, V., 2010, “High-Temperature Elastic Moduli of Bulk Nanostructured n- and p-Type Silicon Germanium,” Phys. Rev. B, 82 (4), p. 045209.  [CrossRef]
34
Reiter, T., and Dvorak, G. J., 1998, “Micromechanical Models for Graded Composite Materials: II. Thermomechanical Loading,” J. Mech. Phys. Solids, 46 (9), pp. 1655–1673.  [CrossRef]
35
Slack, G. A., and Bartram, S. F., 1975, “Thermal Expansion of Some Diamondlike Crystals,” J. Appl. Phys., 46 (1), pp. 89–98.  [CrossRef]
36
Okada, Y., and Tokumaru, Y., 1984, “Precise Determination of Lattice Parameter and Thermal Expansion Coefficient of Silicon Between 300 and 1500 K,” J. Appl. Phys., 56 (2), pp. 314–320.  [CrossRef]
37
Reeber, R. R., and Wang, K., 1996, “Thermal Expansion and Lattice Parameters of Group IV Semiconductors,” Mater. Chem. Phys., 46 (2–3), pp. 259–264.  [CrossRef]
38
Chen, G., 2005, "Nanoscale Energy Transport and Conversion: A Parallel Treatment of Electrons, Molecules, Phonons, and Photons", Oxford University Press, Oxford.
39
Picu, R. C., Borca-Tasciuc, T., and Pavel, M. C., 2003, “Strain and Size Effects on Heat Transport in Nanostructures,” J. Appl. Phys., 93 (6), pp. 3535–3539.  [CrossRef]
40
Xu, Y., and Li, G., 2009, “Strain Effect Analysis on Phonon Thermal Conductivity of Two-Dimensional Nanocomposites,” J. Appl. Phys., 106 (11), p. 114302.  [CrossRef]
41
Born, M., and Huang, K., 1954, "Dynamical Theory of Crystal Lattices", Clarendon, Oxford.
42
Slack, G. A., 1979, “The Thermal Conductivity of Nonmetallic Crystals,” Solid State Phys., 34 , pp. 1–71.  [CrossRef]
43
Majumdar, A., 1993, “Microscale Heat Conduction in Dielectric Thin Films,” ASME J. Heat Transfer, 115 (1), pp. 7–16.  [CrossRef]
44
Ostoja-Starzewski, M., 2006, “Material Spatial Randomness: From Statistical to Representative Volume Element,” Probab. Eng. Mech., 21 , pp. 112–132.  [CrossRef]
45
Rieger, M. M., and Vogl, P., 1993, “Electronic-Band Parameters in Strained Si1 − x Gex Alloys on Si1 − y Gey Substrates,” Phys. Rev. B, 48 , pp. 14276–14287.  [CrossRef]
46
Ravich, Y. I., Efimova, B. A., and Tamarchenko, V. I., 1971, “Scattering of Current Carriers and Transport Phenomena in Lead Chalcogenides,” Phys. Status Solidi B, 43 , pp. 11–33.  [CrossRef]
47
Levinshtein, M. E., Rumyantsev, S. L., and Shur, M. S., eds., 2001, "Properties of Advanced Semiconductor Materials: GaN, AlN, InN, BN, SiC, SiGe", John Wiley & Sons, New York, pp. 149–187.
48
Zawadzki, W., and Szymanska, W., 1971, “Elastic Electron Scattering in InSb-Type Semiconductors,” Phys. Status Solidi B, 45 , pp. 415–432.  [CrossRef]
49
Lundstrom, M., 2000, "Fundamentals of Carrier Transport", Cambridge University Press, Cambridge, UK.
50
Dismukes, J. P., Ekstrom, L., Steigmeier, E. F., Kudman, I., and Beers, D. S., 1964, “Thermal and Electrical Properties of Heavily Doped Ge-Si Alloys Up to 1300 °K,” J. Appl. Phys., 35 (10), pp. 2899–2907.  [CrossRef]

Figures

Grahic Jump Location
+Si1− x Gex unit cell
View Large  |  Save Figure  |  Download Slide (.ppt)
Si1− x Gex unit cell
Figure 2

Si1− x Gex unit cell

Grahic Jump Location
+(a) V-shaped actuator, (b) U-shaped actuator, and (c) Si/Ge nanocomposite material
View Large  |  Save Figure  |  Download Slide (.ppt)
(a) V-shaped actuator, (b) U-shaped actuator, and (c) Si/Ge nanocomposite material
Figure 1

(a) V-shaped actuator, (b) U-shaped actuator, and (c) Si/Ge nanocomposite material

Grahic Jump Location
+Maximum vertical displacement of the U-shaped TA as a function of the length of the Si/Ge nanocomposite for different Ge atomic percentages
View Large  |  Save Figure  |  Download Slide (.ppt)
Maximum vertical displacement of the U-shaped TA as a function of the length of the Si/Ge nanocomposite for different Ge atomic percentages
Figure 17

Maximum vertical displacement of the U-shaped TA as a function of the length of the Si/Ge nanocomposite for different Ge atomic percentages

Grahic Jump Location
+Variation of the temperature distribution along the upper beam of the U-shaped TA with the length of the Si/Ge nanocomposite and the Ge atomic percentage
View Large  |  Save Figure  |  Download Slide (.ppt)
Variation of the temperature distribution along the upper beam of the U-shaped TA with the length of the Si/Ge nanocomposite and the Ge atomic percentage
Figure 16

Variation of the temperature distribution along the upper beam of the U-shaped TA with the length of the Si/Ge nanocomposite and the Ge atomic percentage

Grahic Jump Location
+Maximum displacement of the V-shaped TA for different atomic percentages of Ge in Si1− x Gex
View Large  |  Save Figure  |  Download Slide (.ppt)
Maximum displacement of the V-shaped TA for different atomic percentages of Ge in Si1− x Gex
Figure 15

Maximum displacement of the V-shaped TA for different atomic percentages of Ge in Si1− x Gex

Grahic Jump Location
+Temperature distribution along the V-shaped TA beam for different atomic percentages of Ge in Si1− x Gex (Lc  = 200 μm)
View Large  |  Save Figure  |  Download Slide (.ppt)
Temperature distribution along the V-shaped TA beam for different atomic percentages of Ge in Si1− x Gex (Lc  = 200 μm)
Figure 14

Temperature distribution along the V-shaped TA beam for different atomic percentages of Ge in Si1− x Gex (Lc  = 200 μm)

Grahic Jump Location
+Maximum displacement of the V-shaped TA for different lengths of the Si80 Ge20 nanocomposite
View Large  |  Save Figure  |  Download Slide (.ppt)
Maximum displacement of the V-shaped TA for different lengths of the Si80 Ge20 nanocomposite
Figure 13

Maximum displacement of the V-shaped TA for different lengths of the Si80 Ge20 nanocomposite

Grahic Jump Location
+Variation in the temperature distribution along the V-shaped TA beam with respect to the length of the Si80 Ge20 nanocomposite
View Large  |  Save Figure  |  Download Slide (.ppt)
Variation in the temperature distribution along the V-shaped TA beam with respect to the length of the Si80 Ge20 nanocomposite
Figure 12

Variation in the temperature distribution along the V-shaped TA beam with respect to the length of the Si80 Ge20 nanocomposite

Grahic Jump Location
+Tip displacement of the V-shaped TA as a function of the length of the nanocomposite part and the atomic percentage of Ge in Si1− x Gex
View Large  |  Save Figure  |  Download Slide (.ppt)
Tip displacement of the V-shaped TA as a function of the length of the nanocomposite part and the atomic percentage of Ge in Si1− x Gex
Figure 11

Tip displacement of the V-shaped TA as a function of the length of the nanocomposite part and the atomic percentage of Ge in Si1− x Gex

Grahic Jump Location
+Temperature distribution variation with respect to the length of the nanocomposite part and the atomic percentage of Ge in Si1− x Gex
View Large  |  Save Figure  |  Download Slide (.ppt)
Temperature distribution variation with respect to the length of the nanocomposite part and the atomic percentage of Ge in Si1− x Gex
Figure 10

Temperature distribution variation with respect to the length of the nanocomposite part and the atomic percentage of Ge in Si1− x Gex

Grahic Jump Location
+Temperature-dependent electrical conductivity of the Si1− x Gex nanocomposites for different atomic percentages of Ge
View Large  |  Save Figure  |  Download Slide (.ppt)
Temperature-dependent electrical conductivity of the Si1− x Gex nanocomposites for different atomic percentages of Ge
Figure 9

Temperature-dependent electrical conductivity of the Si1− x Gex nanocomposites for different atomic percentages of Ge

Grahic Jump Location
+Temperature-dependent electrical conductivity of the Si70 Ge30 alloy and the Si80 Ge20 nanocomposites
View Large  |  Save Figure  |  Download Slide (.ppt)
Temperature-dependent electrical conductivity of the Si70 Ge30 alloy and the Si80 Ge20 nanocomposites
Figure 8

Temperature-dependent electrical conductivity of the Si70 Ge30 alloy and the Si80 Ge20 nanocomposites

Grahic Jump Location
+Variation of phonon thermal conductivity of Si1− x Gex nanocomposites at 300 K with respect to the atomic percentage of Ge
View Large  |  Save Figure  |  Download Slide (.ppt)
Variation of phonon thermal conductivity of Si1− x Gex nanocomposites at 300 K with respect to the atomic percentage of Ge
Figure 7

Variation of phonon thermal conductivity of Si1− x Gex nanocomposites at 300 K with respect to the atomic percentage of Ge

Grahic Jump Location
+Strain and temperature dependent phonon thermal conductivity of the Si80 Ge20 nanocomposite between 300 K–800 K
View Large  |  Save Figure  |  Download Slide (.ppt)
Strain and temperature dependent phonon thermal conductivity of the Si80 Ge20 nanocomposite between 300 K–800 K
Figure 6

Strain and temperature dependent phonon thermal conductivity of the Si80 Ge20 nanocomposite between 300 K–800 K

Grahic Jump Location
+Strain and temperature dependent phonon thermal conductivity of bulk Si between 300 K –800 K
View Large  |  Save Figure  |  Download Slide (.ppt)
Strain and temperature dependent phonon thermal conductivity of bulk Si between 300 K –800 K
Figure 5

Strain and temperature dependent phonon thermal conductivity of bulk Si between 300 K –800 K

Grahic Jump Location
+Linear thermal expansion coefficient of Si1− x Gex between 300 K– 800 K
View Large  |  Save Figure  |  Download Slide (.ppt)
Linear thermal expansion coefficient of Si1− x Gex between 300 K– 800 K
Figure 4

Linear thermal expansion coefficient of Si1− x Gex between 300 K– 800 K

Grahic Jump Location
+Elastic constants of Si1− x Gex
View Large  |  Save Figure  |  Download Slide (.ppt)
Elastic constants of Si1− x Gex
Figure 3

Elastic constants of Si1− x Gex

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Evaluation of the Analytical Bottom-Up SIL Proof by Statistical Top-Down Methods (PSAM-0242)
Proceedings of the Eighth International Conference on Probabilistic Safety Assessment & Management (PSAM)
Ceramic and Other Hard Coatings
Tribology of Mechanical Systems> Chapter 9
Experimental Investigation of an Improved Thermal Response Test Equipment for Ground Source Heat Pump Systems
Inaugural US-EU-China Thermophysics Conference-Renewable Energy 2009 (UECTC 2009 Proceedings)
Chitosan-Based Drug Delivery Systems
Chitosan and Its Derivatives as Promising Drug Delivery Carriers> Chapter 4
Liquid Cooled Systems
Thermal Management of Telecommunications Equipment> Chapter 9
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In