If the average heat flux from a microprocessor is 100 W/cm2, what is the maximum thickness of thermal interface material (TIM) that can be tolerated if the maximum temperature drop between the device-side of the die and the heat sink is 50 K? Consider both the temperature drop created by the heat flow through the Si die and the thermal interface material. You can assume that the thermal conductivity of Si is L = 1 W/cm-K and that the thermal conductivity of the TIM is 0.02 W/cm-K. The thickness of the Si die is 600 microns.
If the size of the heat source is smaller than the thickness of the substrate, the temperature rise can be estimated from
DT =
P
2
Ö
p
r0 L
(1)
where r0 is the radius of the heat source, L is the thermal conductivity, and P is the power. Assuming L = 1 W/cm-K, what is the maximum power that can be tolerated in a r0=50 micron spot if the maximum temperature excursion of the device must be limited to 50 K?
Draw the Wigner-Seitz primitive cells for graphene in real space and reciprocal space. Show the correct relative orientation of the primitive cells and give the dimensions of the primitive cells. For the Brillouin zone, give the distance between the origin (G point) and the K and M points. The carbon-carbon bond length in graphene is 0.142 nm.
Using Eq. 2 of Chapter 19 of RW, show that the dispersion at the K point is linear as a function of ky. In this equation, ky is the direction to the K point. (The drawings in this chapter have kx as the direction to the K point.)
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