$$\Delta T_j \;=\; P \sum_{i=1}^{N} R_{\mathrm{th},i}$$

Equation 5 · AI Hardware & Semiconductors

Comparing the Main Approaches to Chiplets and Advanced Packaging

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

The bill for that proximity arrives as heat, and it arrives in a specific, structural way rather than as a vague “3D runs hotter” intuition. A stack has exactly one face in contact with the package’s heat-removal path — typically the topmost die, under a lid or heat spreader — so the temperature rise at a given tier depends on everything the heat has to cross to reach that face: $\Delta T_j \;=\; P \sum_{i=1}^{N} R_{\mathrm{th},i}$. where P is the power dissipated at that tier and each $R_{\mathrm{th},i}$ is the thermal resistance of one layer already between that tier and the heat sink — die bulk, bonding interface, or an intervening active tier. A tier two layers from the heat-removal face inherits the resistance of…

Meanings in this article

• $P$: the power dissipated at that tier and each $R_{\mathrm{th},i}$ is the thermal resistance of one layer already between that tier and the heat sink — die bulk, bonding interface, or an intervening active tier.
• $R_{\mathrm{th},i}$: the thermal resistance of one layer already between that tier and the heat sink — die bulk, bonding interface, or an intervening active tier.

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