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 Zhou CS Department, Tsinghua University, Beijing.,etc. ICCAD 2007

Outline Introduction Previous Works Algorithm Experimental Results Conclusions

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 n L-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 with 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

Adaptive Three-Stage Flow

Force-Directed Techniques Assume each layer and each block has the same thickness D Blocks connected by virtual springs c ij is the weight of the connection Combine the c ij coefficients in to a global stiffness matrix C Solve the three systems of equations to obtain the coordinate of each block

The Forces Filling Force: f x F, f y F, f z F 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 prorated Filling Forces of the bins the cell covers Thermal Force: f x T, f y T, f z T 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 α x,y,z : influence the amount of block displacement per iteration resulting β x,y,z : adjust the percentages between Filling Force and Thermal Force These parameters are experimentally determined, but are general

Adaptive Three-Stage Flow

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 near the heatsink Benefits of the initial 2D lateral spreading Evenly distribute lateral power density Overlaps are controlled to support subsequent 3D optimization

Adaptive Three-Stage Flow

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

Adaptive Three-Stage Flow

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 overlap 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

Adaptive Three-Stage Flow

Legalization After force-directed iterations cease, residual overlaps remain Use topological relations between overlapping blocks to minimize displacement Similar to [20] Permit block rotation

Experimental Results Effects of Optimization Stages

Comparison with CBA CBA [12] “A Thermal-driven floorplanning algorithm for 3D ICs” Temperature-aware 3D floorplanning Handled heterogeneous blocks Simulated annealing based

Power Distribution Power distribution during each optimization stage for n100

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

Conclusions They modified the traditional forced-directed technique flow, to smooth the transition from a 3D placement to a layer-assigned floorplan The closed feedback loop between temperature and leakage power consumption is modeled Less run time, compare with precious works