Problem A square silicon chip (k = 150 W/mK) is of width w = 6 mm on a side and of thickness t = 1 mm. The chip is mounted in a substrate such that its side and back surfaces are insultated, while the front surface is exposed to a coolant. If 12 W are being dissipated in circuits mounted to the back surface of the chip, what is the steady-state temperature difference between back and front surfaces.
Solution The temperature difference would be T1 − T2, or ΔT
Assumptions: • steady-state conditions
• constant properties
• uniform heat dissipation
• negligible heat loss from back and sides
• one-dimensional conduction in chip
The electrical power dissipated at the back surface of the chip is transferred by conduction through the chip. Therefore, from Fourier's law:
