TSV-Constrained Micro-Channel Infrastructure
Design for Cooling Stacked 3D-ICs
Bing Shi and Ankur Srivastava, University of Maryland, College
Park, MD, USA
ISPD 2012
Outline
• Introduction and Motivation• Thermal and Power model with micro-
channels• Formulation and Micro-channel
design algorithms• Experimental results• Conclusions
Introduction
• Conventional air cooling might be not enough for stacked 3D-ICs.– Micro-channel based liquid cooling is
developed.
• Micro-channel heat sinks are embedded below each silicon layer and the coolant fluid is pumped through the micro-channels.
Schematics
Effectiveness
Motivating example
• Conventionally, straight channels are used.– But TSVs will block the route of straight
channels.
Introduction (cont.)
• With bended structure, the micro-channels can reach those TSV-blocked hotspot regions which straight micro-channels cannot reach.
• Compared to straight channel design, up to 87% pumping power could be saved.
Thermal and Power model with micro-channels
• Thermal modeling– Use RC network to represent.– Steady states: pure resistive network.– Solve GT=Q, where G is the thermal conductivity
matrix and Q is the power profile.• G depends on many factors including the
material properties, location of channels and TSVs, fluid flow rate etc.
• Hotspot is the location that its temperature T is greater than maximum temperature constraint .
Micro-channel power consumption• Pumping power
– where N is the total number of channels, and are the pressure drop and fluid flow rate of the n-th micro-channel.
• Laminar liquid flow– pressure drop in a straight micro-channel – L is the length of micro-channel, is hydraulic
diameter, v is fluid velocity, μ is fluid viscosity and γ is determined by the micro-channel dimension.
Fluid flow rate
• Fluid flow rate – are the channel width and height.
• Flow rate could be controlled by changing the pressure drop.
• Usually fluid pumps are designed to work such that all the micro-channels experience the same pressure drop.– So that higher pressure drop results in
higher flow rate and better cooling.
Modeling Micro-channels with bends
• Three types of region– Fully developed laminar flow region.– The bend corner.– The developing/turbulent region after the
bend.
Pressure drop
• Pressure drop in fully developed region
• Pressure drop in developing region
• Pressure drop in corner region
• Total pressure drop
– A quadratic function of v.
Total pumping power
• Solve the equation for fluid velocity.• Estimate the fluid flow rate f, and thus
estimate the thermal resistance and pumping power for this channel.
• Hence, the pumping power as well as cooling effectiveness of micro-channels with bends is a function of– Number of bends.– Location of channels.– Pressure drop across the channel.
• Slower velocity means lower cooling efficiency.– More pumping power is needed.
Problem to be solved
• To find micro-channel routes from one side to the other such that– The routes do not intersect.– Avoid TSVs.– Provide sufficient cooling at
minimum pumping energy.
Represent the routing problem
• Each grid on the layout is a node.• Edge exists if
– Two nodes are adjacent.– Non of them is a TSV.
• Formulate the problem Minimize pumping power
I/O nodes
Routable nodes
TSV constraints
Temperature constraints
Edge constraints
The same edge
The grid graph
But…
• This is a very complex problem since – The variables need to be discrete.– The thermal and pumping power models
are highly nonlinear.• Propose a min-cost flow based
method to do the job.
Overall flow
• The flow– Full scale thermal analysis.– Initial micro-channel design– Iterative refinement with thermal
analysis
Min-cost flow based micro-channel design
• Initialization– I/O nodes are assigned a supply/demand
of one flow unit.– All nodes in the grid graph have a
capacity one.– The edges have unlimited capacity and
are bi-directional.• Assigning the node capacity to be 1
would ensure that all the flow from inlet to outlet follows simple paths (non-intersecting and non-cyclic).
Cooling demand
• A silicon layer would be cooled by the micro-channels both above and below.– Unless the silicon layer is at the very top
or very bottom of the stack.• For a location that need cooling.
– is the heat load partitioning factor.– cooling demand assigned to the top.– cooling demand assigned to the bottom.
Cooling demand (cont.)
• The top(bottom)-most layer only cooled by its bottom(top) micro-channel.– is set to 0(1) accordingly.
• Otherwise, is set according to the ratio of number of TSVs in the adjacent layer.– Less TSVs, more space for micro-channel.
Cost assignment
• Higher demand leads to lower cost since we would like micro-channels to pass through high cooling demand regions.
• Let be the heat load partitioning factor of grid on silicon layer , .
Cost assignment (cont.)
• If the hotspot exists in both side
• If the hotspot only exists in one side
• If the hotspot does not exist in both side– The node cost is assigned to a
small positive value
Micro-channel refinement
• Two situation that degrade the cooling quality.– Some channels have several
bends.– It may be routed over
disproportionately large number of hotspots.
• Iteratively refine the results
How to get the minimum required pumping power
• Linearly increase the pressure drop until the temperature met the goal.
Iterative micro-channel optimization
• The objective of minimum cost flow formulation did not capture cooling energy and/or number of bends in the channels.
• Such imbalance (in cooling demand and bend count) leads to increase in the required pressure drop and thereby increasing the pumping energy.
Iterative micro-channel optimization (cont.)
• The basic idea is that all the channels should have similar levels of heat load, length and number of bends.
• Based on these considerations, the initial design is refined by– Balancing the heat loads among
micro-channels.– Reducing unnecessary bends.
Iterative micro-channel optimization (cont.)
• Micro-channel heat load balancing:
Iterative micro-channel optimization (cont.)
• Bend Elimination– Identify all unnecessary bends and
replace them with equivalent straight channels or patterns with lesser corners.
– Removing corners in the hotspot region might lead to reduction in the cooling performance.
– Only remove those corners in the non-hotspot regions which can easily be identified by the thermal analysis.
Experimental setting
• Two-tier stacked 3D-IC with 4-core CPU on each.– Different number of TSVs which are
randomly distributed.• SPEC 2000 CPU benchmarks
– Simulate 20 such benchmarks to get power profile and randomly choose 4 of these profiles to compose a one-tier profile.
• Combine two of these power profiles to form a two-tier profile.
Parameters
• The area of each chip stack is • The grid size is (so grids in each layer).• The channel dimensions are .• The maximum temperature constraint .• The maximum available pressure drop is
500kPa.
Experimental results (cont.)
• Uses 20 micro-channels.
Conclusions
• Micro-channel cooling will be needed in the near future.
• Proposes a flow which designs TSV-constrained micro-channel infrastructure.
• Up to 87% pumping power saving compared with the micro-channel structure using straight channels.