Equation 1 · Part 8 · Chiplets and Advanced Packaging in Practice: Floorplanning, UCIe, and Thermal Co-Design

Symbol sigma_max

\text{Cost}(\mathcal{P}) \;=\; \alpha \cdot WL(\mathcal{P}) \;+\; \beta \cdot T_{\max}(\mathcal{P}) \;+\; \gamma \cdot \sigma_{\max}(\mathcal{P}),

\sigma_{\max}

What this part means

peak mechanical stress at any bonded interface.

Its job in the formula

sigm $a_m$ ax appears in the objective or constraint used by the optimization on the right.

Full expressionSymbol sigma_maxArticle meaning

Where the article explains it

where $\mathcal{P}$ is a candidate placement of dies on the carrier, WL is total interconnect wirelength, $T_{\max}$ is peak steady-state junction temperature anywhere in the assembly, and $\sigma_{\max}$ is peak mechanical stress at any bonded interface.

The passage around this formula

…a single term: $\text{Cost}(\mathcal{P}) \;=\; \alpha \cdot WL(\mathcal{P}) \;+\; \beta \cdot T_{\max}(\mathcal{P}) \;+\; \gamma \cdot \sigma_{\max}(\mathcal{P})$ . where $\mathcal{P}$ is a candidate placement of dies on the carrier, WL is total interconnect wirelength, $T_{\max}$ is peak steady-state junction temperature anywhere in the assembly, and $\sigma_{\max}$ is peak mechanical stress at any bonded interface. This is a schematic statement of the shape these tools optimize, not a reproduction of any one paper’s exact formula, but it makes the practitioner point concrete: whichever of $\alpha$ , $\beta$ , and $\gamma$ a design team weights most…

Read this part in the article →

Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.