3D-STAF: Scalable Temperature and Leakage Aware Floorplanning for Three-Dimensional Integrated...
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Transcript of 3D-STAF: Scalable Temperature and Leakage Aware Floorplanning for Three-Dimensional Integrated...
3D-STAF: Scalable Temperature and Leakage Aware Floorplanning for Three-Dimensional
Integrated Circuits
Pingqiang Zhou, Yuchun Ma, Zhouyuan Li, Robert P. Dick, Li Shang, Hai Zhou,
Xianlong Hong, Qiang ZhouCS Department, Tsinghua University, Beijing.,etc.
ICCAD 2007
Three-dimensional integration
Stack silicon dies connected through inter-die vias
Can be used to decrease wire delay, increase integration density, improve performance, and reduce power consumption
But, thermal effects become a problem
Challenges of 3D IC Floorplanning
Design space explosion The solution space of 3D floorplanning increases
by nL-1/(L-1)! times compared to the 2D cases Multi-objective optimization
Minimization of temperature complicates the optimization of area, wirelength, leakage power
Temperature-leakage dependency Subthreshold leakage increases superlinearly wit
h temperature
Previous Works
SA based stochastic optimization techniques Capable of handling heterogeneous blocks Long runtimes that scale poorly with problem size
Force-directed temperature-aware standard-cell placement Simultaneous temperature feedback to blocks Scalable performance NOT capable of handling heterogeneous blocks
Traditional Algorithm Flow
Optimize peak temperature, area, wirelength, and via count
Small local changes may cause significant changes to the global solution
Force-Directed Techniques
Assume each layer and each block has the same thickness D
Blocks connected by virtual springs
cij is the weight of the connection Combine the cij coefficients in to a global stiff
ness matrix C Solve the three systems of equations to obtai
n the coordinate of each block
The Forces
Filling Force: fxF, fy
F, fzF
To eliminate overlap between blocks and distribute them evenly
The Filling Force of each bin is equal to its bin density A block receives a Filling Force equal to the sum of the pro
rated Filling Forces of the bins the cell covers
Thermal Force: fxT, fy
T, fzT
To move blocks which produce heat away from regions of high temperature
Using the thermal gradient to determine directions and magnitudes of the Thermal Forces on blocks Extract power density information into thermal analyzer
Aggregate Forces
αx,y,z: influence the amount of block displacement per iteration resulting
βx,y,z: adjust the percentages between Filling Force and Thermal Force
These parameters are experimentally determined, but are general
2D Temperature-Aware Lateral Spreading
Traditionally, the initial optimization is influenced primarily by overlap instead of thermal effects Some cool blocks with large areas to be pushed n
ear the heatsink Benefits of the initial 2D lateral spreading
Evenly distribute lateral power density Overlaps are controlled to support subsequent 3D
optimization
Global Optimization in Continuous 3D Space
Allow arbitrary motion in continuous 3D space
Compute power density distribution for each layer to obtain thermal gradient Stochastic mapping of blocks to layer
Thermal Analysis and Continuous 3D Force-Directed Phase
Use stochastic layer assignment results for thermal analysis The positions are only temporarily discretized
Repeat force-directed move
Layer Assignment
Assign an area budget to each layer Start from the layer closest to the heatsink
Attempt to assign blocks as low as possible
Attempt to honor via count constraint Avoid assignments to layers violating area budget Choose one of three nearest layers with minimal ov
erlap with previously-assigned blocks
Optimization with Layer Assignment
In this stage, every block is assigned to one layer according to the current placement
The thermal model can be used to compute temperature gradients and Thermal Force
The changes in positions caused by layer assignment lead the subsequent force-directed iterations to adjust the placement
The optimization process ultimately converges to the final multi-layer floorplan
Legalization
After force-directed iterations cease, residual overlaps remain
Use topological relations between overlapping blocks to minimize displacement Similar to [20]
Permit block rotation
Comparison with CBA
CBA [12] “A Thermal-driven floorplanning algorithm for
3D ICs” Temperature-aware 3D floorplanning Handled heterogeneous blocks Simulated annealing based
Leakage Power Consumption Analysis
Higher temperatures increase leakage power, which in turn further increases temperature
Impact of Leakage Power-Temperature Feedback Loop
3D-STAF: the interdependence of temperature and leakage are neglected Temp: the peak temperature estimated when the
dependence of leakage on temperature is ignored Temp (feedback): the feedback loop is considered
3D-STAF-TDLP: the interdependence is considered