Equation 1 · Chiplets and Advanced Packaging in Practice: Floorplanning, UCIe, and Thermal Co-Design
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Symbol P
a candidate placement of dies on the carrier, WL is total interconnect wirelength.
Symbol W
W appears in the objective or constraint used by the optimization on the right.
Symbol L
L appears in the objective or constraint used by the optimization on the right.
Symbol β
β appears in the objective or constraint used by the optimization on the right.
Symbol gamma
the design team weights most heavily determines where dies actually land.
=
The expressions on both sides represent the same quantity under the stated assumptions.
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The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
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What the article says around this equation
A floorplanning objective built to hold all three properties at once is naturally written as a weighted combination rather than a single term: . where is a candidate placement of dies on the carrier, WL is total interconnect wirelength, is peak steady-state junction temperature anywhere in the assembly, and 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 , , and a design team weights most heavily determines where dies actually land, and a…
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A floorplanning objective built to hold all three properties at once is naturally written as a weighted combination rather than a single term: . where is a candidate placement of dies on the carrier, WL is total interconnect wirelength, is peak steady-state junction temperature anywhere in the assembly, and 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 , , and a design team weights most heavily determines where dies actually land, and a floorplan tuned only for WL is optimizing a real but incomplete objective.
Sources cited in the article section
- [5] TAP-2.5D: A Thermally-Aware Chiplet Placement Methodology for 2.5D Systems ↗
- [4] STAMP-2.5D: Structural and Thermal Aware Methodology for Placement in 2.5D Integration ↗
- [6] Simultaneous Multi-die Floorplanning and Technology Assignment ↗
These citations give research context. Read each source to check which claims it supports.
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