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MICRO/NANOSCALE HEAT TRANSFER—PART II

# Thermal Conductivity Measurements on Polycrystalline Silicon Microbridges Using the $3ω$ Technique

[+] Author and Article Information
Patrick E. Hopkins1

Department of Mechanical and Aerospace Engineering, University of Virginia, P.O. Box 400746, Charlottesville, VA 22904-4746

Leslie M. Phinney2

Engineering Sciences Center, Sandia National Laboratories, P.O. Box 5800, Albuquerque, NM 87185-0346lmphinn@sandia.gov

1

Present address: Engineering Sciences Center, Sandia National Laboratories, P.O. Box 5800, Albuquerque, NM 87185-0346.

2

Corresponding author.

J. Heat Transfer 131(4), 043201 (Feb 11, 2009) (8 pages) doi:10.1115/1.3072907 History: Received March 27, 2008; Revised December 09, 2008; Published February 11, 2009

## Abstract

The thermal performance of microelectromechanical systems devices is governed by the structure and composition of the constituent materials as well as the geometrical design. With the continued reduction in the characteristic sizes of these devices, experimental determination of the thermal properties becomes more difficult. In this study, the thermal conductivity of polycrystalline silicon (polysilicon) microbridges are measured with the transient $3ω$ technique and compared with measurements on the same structures using a steady state Joule heating technique. The microbridges with lengths from $200 μm$ to $500 μm$ were designed and fabricated using the Sandia National Laboratories SUMMiT V™ surface micromachining process. The advantages and disadvantages of the two experimental methods are examined for suspended microbridge geometries. The differences between the two measurements, which arise from the geometry of the test structures and electrical contacts, are explained by bond pad heating and thermal resistance effects.

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## Figures

Figure 1

Optical microscope image of a 10 μmwide×200 μm long test structure fabricated using the SUMMiT V™ process. The bond pads are 100 μm wide and 300 μm long. Two wires bonded to bond pad are visible in the image. The connections to the package are outside of the image.

Figure 2

Schematic representing circuit and data acquisition equipment in the 3ω measurements. The sample is the polysilicon microbridge structure, and the fixed resistance varied depending on the sample. The value of the fixed resistance was chosen to be slightly higher than the maximum resistance across the sample (14). During testing, this value was set to be slightly higher than the room temperature resistance of the sample.

Figure 3

Sensitivity of Eq. 1 to the thermal time constant γ. A best fit thermal conductivity k is 66 W m−1 K−1. The thermal conductivity of the test structures is easily determined by identifying the region of frequency independent V3ω and fitting Eq. 2 to the data.

Figure 4

3ω voltage on the different length bridge structures with the Eq. 1 fit to the data with best fit k and γ. The data and best fit are normalized for clarity. The frequency independent region of the 3ω voltage responses increases with a decrease in temperature.

Figure 5

Thermal time constant γ as a function of bridge length L determined at two different temperatures

Figure 6

Thermal conductivity measured with the 3ω (filled squares) and steady state (empty circles) (11) techniques as a function of bridge length at four different temperatures. The dependency of the data on bridge length is shown by the slope of the best fit line to the data. The bridge length dependency is essentially nonexistent in the lower temperature 3ω data, which is apparent by comparing the thermal conductivity trends with bridge length represented by the slopes of the best fit line to the data that are listed in the figures.

Figure 7

Temperature dependent thermal conductivity data on the polysilicon bridge test structures. The 3ω and steady state measurements are both presented for comparison. The differences between the two sets of data determined from the different measurement techniques can be explained by the effects of bond pad heating and thermal boundary resistance between the Al wire bonded film and the bond pad.

Figure 8

Additional thermal resistances determined from the two data sets in Fig. 7 and Eq. 7 compared with the predicted thermal resistance Rpredicted of the 700 nm Al bond pad the Al/Si interface

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