Feeds:
Posts

## Semiconductors in electronical devices – Thermal Metrics

During the work regarding my PhD I found a nice paper that explains some thermal metrics like the junction temperature $T_J$ the case temperature $T_C$, the ambient temperature $T_A$ and the corresponding thermal resistances. This is done with an example of a coffee-cup. It’s that nice and memorable that I want to post this explanation here. I took it from an Texas Instrument’s Application Report with the title “Thermal Derating Curves for Logic-Products Packages from May 2009. You can find the whole paper here. You can find also a nice picture of the coffee-cup and the metrics in the paper.

“Consider a closed cup of heated coffee at a certain temperature (see Figure 1). The temperature of the coffee is analogous to the junction temperature ($T_J$) of a semicondutor device. The outer surface of the coffee cup is at some temperature analogous to the temperature of the outside of the semiconductor package, or case temperature, ($T_C$). Finally, the room is at ambient, or free-air, temperature ($T_A$). Clearly, $T_J > T_C > T_A$.

Heat transfers from the coffee through the cup by conduction. Thus, there is a temperature differential between the coffee and the outer surface. The rate of heat transfer through the cup is determined by the thermal resistance of the walls of the cup. The thermal resistance is a function of the material used to make the cup (e.g., paper, Styrofoam (trademark of Dow Chemical Company), or porcelain), the thickness of the walls of the cup, and the overall geometry of the cup. The higher the thermal resistance, the slower the heat travels through the cup. The thermal resistance between the junction (the coffee) and the case (cup) can be designated $\Theta_{JC}$.

Moving away from the junction, heat then transfers from the surface of the cup by radiation and convection. There is a thermal resistance associated with this transfer that is expected to be a function of the geometry, smoothness, and color of the surface. This thermal-resistance value is termed $\Theta_{CA}$.

The overall rate of heat transfer is then a combination of $\Theta_{JC}$ and $\Theta_{CA}$. There is a temperature drop (much like a voltage drop) from the inner side to the outer side of the cup and another drop from the surface of the cup to the ambient environment. Of course, the objective is to keep coffee warm. But, with semiconductors, the objective is to move heat away from the IC chip as quickly as possible.”