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Thermal Analysis 335
All dimensions are in millimeters.
Die thickness = 2 mm
Substrate thickness = 2 mm
40.000
20.000
Copper die
20.000
Silicon substrate
40.000
9.10 The following square platform with two arms has a thickness of 1 mm and is
made of silicon with a thermal conductivity k = 130 W/(m°C), Young’s modu-
lus E = 200 GPa, Poisson’s ratio ν = 0.27, and thermal expansion coefficient
−6
α = 2.6 × 10 /°C. Ignore the effects of convective heat transfer. (1) Determine the
temperature distribution in the platform when the temperatures of the upper
and lower ends are set uniform at 40°C and 20°C, respectively, as shown below.
(2) Suppose the ends of the two arms are fixed. Determine the thermally induced
deformation and stresses in the platform.
T upper = 40°C All dimensions are in centimeters.
1.000 12.000
1.000 1.000
10.000
1.000
1.000
10.000
12.000 1.000
T lower = 20°C
