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Micro/Nanoscale Heat Transfer

Scaling of Thermal Positioning in Microscale and Nanoscale Bridge Structures

[+] Author and Article Information
Elham Maghsoudi

 Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803emaghs1@lsu.edu

Michael James Martin

 Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803

J. Heat Transfer 134(10), 102401 (Aug 07, 2012) (7 pages) doi:10.1115/1.4006661 History: Received May 02, 2011; Revised April 13, 2012; Published August 06, 2012; Online August 07, 2012

Heat transfer in a thermally positioned doubly clamped bridge is simulated to obtain a universal scaling for the behavior of microscale and nanoscale bridge structures over a range of dimensions, materials, ambient heat transfer conditions, and heat loads. The simulations use both free molecular and continuum models to define the heat transfer coefficient, h. Two systems are compared: one doubly clamped beam with a length of 100 μm, a width of 10 μm, and a thickness of 3 μm, and a second beam with a length of 10 μm, a width of 1 μm, and a thickness of 300 nm, in the air at a pressure from 0.01 Pa to 2 MPa. The simulations are performed for three materials: crystalline silicon, silicon carbide, and chemical vapor deposition (CVD) diamond. The numerical results show that the displacement and the response of thermally positioned nanoscale devices are strongly influenced by ambient cooling. The displacement depends on the material properties, the geometry of the beam, and the heat transfer coefficient. These results can be collapsed into a single dimensionless center displacement, δ*  = δk/q″αl2 , which depends on the Biot number and the system geometry. The center displacement of the system increases significantly as the bridge length increases, while these variations are negligible when the bridge width and thickness change. In the free molecular model, the center displacement varies significantly with the pressure at high Biot numbers, while it does not depend on cooling gas pressure in the continuum case. The significant variation of center displacement starts at Biot number of 0.1, which occurs at gas pressure of 27 kPa in nanoscale. As the Biot number increases, the dimensionless displacement decreases. The continuum-level effects are scaled with the statistical mechanics effects. Comparison of the dimensionless displacement with the thermal vibration in the system shows that CVD diamond systems may have displacements that are at the level of the thermal noise, while silicon carbide systems will have a higher displacement ratios.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

The geometry and boundary conditions in the model

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Figure 2

Displacement variations along the length of the bridge for different heat fluxes in MEMS beam (free molecular method—Bi = 3.162 × 10−6 )

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Figure 3

Center displacement variation by pressure: (a) Silicon microscale, (b) silicon nanoscale, (c) silicon carbide nanoscale, and (d) CVD diamond nanoscale

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Figure 4

Dimensionless temperature difference versus the Biot number for various materials

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Figure 5

Dimensionless displacement versus the Biot number: (a) For various materials and (b) for various bridge lengths

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Figure 6

Thermal displacement versus temperature variations

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Figure 7

DR: (a) For three materials at P = 0.1 Pa (b) silicon carbide-free molecular

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