tsv-aware analytical placement for 3d ic designs meng-kai hsu, yao-wen chang, and valerity balabanov...
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TSV-Aware Analytical Placement for 3D IC Designs
Meng-Kai Hsu, Yao-Wen Chang, and Valerity BalabanovGIEE and EE department of NTU
DAC 2011
Outline
Introduction Previous works and Contributions Problem formulation and analytical
placement TSV-aware 3D analytical global placement TSV insertion and TSV-aware legalization Experimental results and Conclusions
Introduction
3D IC technology can effectively reduce global interconnect length and increase circuit performance.
In a generic 3D IC structure, each die is stacked on top of another and communicated by Through-Silicon Vias (TSVs).
Introduction (cont.)
TSV pitches are very large compared to the sizes of regular metal wires under current technology.
Moreover, TSVs are usually placed at the white space. Routing resource, chip area, yield, etc.
are affected.
Schematic view of placement
Example of placement
If the TSVs are not well considered…
Previous works
[9] folding/stacking with layer re-assignment.
[11] use partitioning-based approach. [7] is multi-level analytical placement
and cell could move along z-direction. [15] partition cell first, then do
placement for each layer.
Contributions
New 3D placement algorithm consists of three stages that takes sizes and positions of TSVs into account.
Weighted-average wirelength model with smaller estimation errors than Log-sum-exp (LSE) model.
Density cube to model the density.
Contributions (cont.)
Not only handles the TSV count but also handles the size of TSVs.
A TSV insertion algorithm based on the overlapping whitespace area between neighboring layers is proposed to determine the location of each TSV.
Routing can be easily accomplished. Moreover, the proposed algorithm achieves best comparing with [7,15].
Problem formulation Given a placement region and the number of device
layers k, we intend to determine the optimal positions of movable blocks so that the total wirelength and the number of required TSVs are minimized while satisfying the non-overlapping constraints among blocks and TSVs.
Inputs as the set of n blocks. as the set of m nets. Placement region definitions with k device layers. Density constraints, TSV size.
Outputs The location of each block and TSVs (layer and coordinates)
without constraint violation. The netlist should be updated.
},...,,{ 21 nvvvV },...,,{ 21 meeeE
Traditional placement flow
Global placement: Find the best position and layer for each block to minimize the target cost.
Legalization: Remove overlaps. Detail placement: Refines the
placement solution.
Analytical placement
Optimize the target of placement by mathematical way. Linear programming (LP), Quadratic
programming (QP), etc.
Key: How to model and how to solve.
Proposed TSV-aware 3D analytical placement flow
3D analytical global placement
The 3D analytical global placement problem can be formulated as a constrained optimization problem as follows:
Wirelength and TSV model
The wirelength W(x, y) is defined as the total half-perimeter wirelength (HPWL).
The number of TSVs used for each net could be approximated by the number of layers it spans.
Wirelength and TSV model (cont.)
The above equations is not differentiable. Need differentiable one to approximate.
Log-sum-exp (LSE) model
The LSE wirelength is close to the HPWL when γ approaches to zero. In fact, γ cannot be too small or else overflow
occurs => error is inevitable.
Proposed weighted-average (WA) wirelength model
Weighted-average
In order to approximate maximum, the following function is used.
Hence, the WA model will be:
Estimation error comparisons
Density cube model
The density of a cube b of layer k can be defined as:
Px, Py, and Pz are the overlap computing functions along three dimensions.
White space reservation for TSVs
Assume that the communication between neighboring layers of a net is through one TSV.
Distribute required spaces for TSVs into density cubes inside the net-box evenly. Net-box: the range spanned by a net.
Transform to unconstrained problem
Solve a sequence of unconstrained problem with increasing λ.
TSV insertion and TSV-aware legalization
Three-step scheme Layer-by-layer standard cell legalization TSV insertion TSV-aware legalization
Layer-by-layer standard cell legalization Minimum cell displacement without considering
TSVs. Just like traditional legalization.
TSV insertion and TSV-aware legalization (cont.)
TSV insertion Decompose each net to 2-pin nets by MST. Start from the 2-pin net with the smallest net-box
to the largest one. Divide the region enclosed by net-box into bins,
and insert TSV into the overlapping white space bin with minimized overlap between cells and TSVs.
If there is not enough white space in the net-box, the searched region is doubled, and the search process continues.
Decompose each net to 2-pin nets by MST
Project cells to a single layer, then compute edge cost by β*L(e)+δ*Z(e).
TSV insertion and TSV-aware legalization (cont.)
TSV-aware legalization Apply step1 and set TSVs as fixed
blocks.
Experimental results
Environment PC workstation 8x Xeon 2.5 GHz CPUs 26 GB memory Implemented using C++
Integrated into NTUplace3 α ,β, and γ are set to 10, 0.4, and 0.6
respectively.
3D analytical placement comparisons
4-layer 3D IC, area of each layer is (original area)/4 and then enlarge to get 10% white space.
TSV-aware placement comparisons
White space reservation comparisons
Example
Wirelength model comparisons
Conclusions
Proposes a new TSV-aware placement algorithm for 3D design.
Weighted-average wirelength model. White space reservation for TSV
insertion. Routing could easily be done by 2D
routers, and the algorithm achieves the best result among [7,15].