Question

4. Through-silicon-via (TSV) has been widely used in electronics, which is a vertical metal via that passes completely through a silicon substrate. Consider a metal TSV embedded in the silicon substrate. The TSV is made from steel and copper, which have the thermal conductivities of ksteel 50 Wm K, and k-400 Wm K. The silicon has a thermal conductivity of ks-100 Wm K-1. The analysis of thermal transport in the TSV-Si composite can start from its unit cell due to periodicity. The figure below shows the top-down view of the unit cell for TSV-Si composite and the thickness (1) of the unit cell is 100 μrm. If 0.1 W heat rate is uniformly applied on the left surface of the unit cell and the right surface of the unit ce is fixed at 40 °C (T2), what is the temperature of the left surface (T)? Note: You can consider other surfaces of the unit cell as adiabatic surfaces. 40 um Adiabc .T T, Lateral direction 1 Cu LI Si Steel B Steel Adiabatic

Answer 1

stive. St 1o all dimustons Reyma 1 conductiv Asumptons (1 )--1-D-heat troustri equivalevd. titult i elestvical-analogy qivae Rs es, Reu Rst

evm te e reepeetvely Rst toy > length to Rei k A yoss seetluo 4000x 25 klw dtng st For k A -12 2 400 klo -12 -12 k A 26 k 8000시012x400

he equvalent Cvcuit is A00 26 MA 2 2 400 pavallal B 400 ADD avo 25 22.22 25.- 2. aquivalourveistams 2.22-k/w ta Re 01 40-T . Tr 32.77

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