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Research Papers

# Correlating Microscale Thermal Conductivity of Heavily-Doped Silicon With Simultaneous Measurements of Stress

[+] Author and Article Information
Ming Gan

Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47906

Vikas Tomar1

Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47906tomar@purdue.edu

1

Corresponding author.

J. Eng. Mater. Technol 133(4), 041013 (Oct 20, 2011) (5 pages) doi:10.1115/1.4004699 History: Received March 31, 2011; Accepted July 12, 2011; Published October 20, 2011; Online October 20, 2011

## Abstract

The functioning and performance of today’s integrated circuits and sensors are highly affected by the thermal properties of microscale silicon structures. Due to the well known size effect, the thermal properties of microscale silicon structures are not the same as those of the bulk silicon. Furthermore, stress/strain inside microscale silicon structures can significantly affect their thermal properties. This article presents the first thermal conductivity measurements of a microscale silicon structure under applied compressive stress at 350 K. Atomic force microscope (AFM) cantilevers made of doped single-crystal silicon were used as samples. A resistance temperature detector (RTD) heater attached to another RTD sensor was used as the heating module, which was mounted onto a nanoindentation test platform. This integrated system applied compressive load to the cantilever in the longitudinal direction while supplying heat. The thermal conductivity of the cantilevers was calculated using steady state heat conduction equation. The result shows that the measured thermal conductivity varies from $110 W/(m·K)$ to $140 W/(m·K)$ as compressive strain varies from 0.1% to 0.3%. Thermal conductivity is shown to increase with increase in compressive strain. These results match with the published simulation values. The measured thermal conductivity and stress values vary in the similar manner as a function of applied strain.

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## Figures

Figure 1

SEM images of the AFM cantilever specimen

Figure 2

Experimental setup of simultaneous compressing and measuring hot and cold temperatures Th and Tc , respectively, to measure thermal conductivity

Figure 3

(a) Load–displacement curve shown corresponds to rounding of the cantilever end indicated by almost zero load and significant displacement. A load of 10 mN maximum was applied in this process and (b) load–displacement curve after the rounding of cantilever end has been performed. The zero load displacement shown in part (a) disappears.

Figure 4

Different load profiles at maximum loads of 10 mN, 20 mN, 30 mN, and 40 mN. (a) Load–displacement plot and (b) stress–strain plot.

Figure 5

Temperature profile of the hot end (Th ) and the cold end (Tc ). For the measurements shown a constant load of 40 mN was applied. The load was held constant for 400 s. The voltage of the heating power is 9 V DC.

Figure 6

Thermal conductivity as a function of strain level for (a) sample set 1 and (b) sample set 2

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