Equation 5 · Part 10 · Comparing the Main Approaches to Chiplets and Advanced Packaging

Starting index or lower bound: i=1

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

i=1

What this part means

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Its job in the formula

i=1 appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

Full expressionStarting index or lower bound: i=1Article meaning

The passage around this formula

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…

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Learn the underlying idea

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

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Sources cited in the article section

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