TSV-Constrained MicroChannel 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 microchannels
• 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
𝑇𝑚𝑎𝑥 .
Micro-channel power consumption
• Pumping power 𝑄𝑝𝑢𝑚𝑝 =
𝑁
𝑛=1 𝑓𝑛 ∆𝑃𝑛
– where N is the total number of channels, ∆𝑃𝑛 and 𝑓𝑛
are the pressure drop and fluid flow rate of the n-th
micro-channel.
• Laminar liquid flow
– pressure drop in a straight micro-channel ∆𝑃 =
2𝛾𝜇𝐿𝑣
𝐷ℎ2
– L is the length of micro-channel, 𝐷ℎ 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 𝑓 = 𝑣𝑤𝑎 𝑤𝑏
– 𝑤𝑎 , 𝑤𝑏 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
– ∆𝑃𝑓 =
2𝛾𝜇𝐿𝑓 𝑣
𝐷ℎ2
• Pressure drop in developing region
– ∆𝑃𝑑 = 𝑚∆𝑝𝑑 = 𝑚𝐾𝑑 𝜌𝑣 2
• Pressure drop in corner region
𝜌
2
– ∆𝑃90° = 𝑚∆𝑝90° = 𝑚𝐾90° 𝑣 2
• Total pressure drop
– ∆𝑃 = ∆𝑃𝑓 + ∆𝑃𝑑 + ∆𝑃90° =
– A quadratic function of v.
2𝛾𝜇𝐿𝑓
𝐷ℎ2
𝑣 + 𝑚𝐾𝑑 𝜌 + 𝑚𝐾90°
𝜌
2
𝑣2
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 bidirectional.
• 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.
– 𝜇 is the heat load partitioning factor.
– 𝜇𝑇 cooling demand assigned to the top.
– (1 − 𝜇)𝑇 cooling demand assigned to the
bottom.
Cooling demand (cont.)
• The top(bottom)-most layer only cooled by
its bottom(top) micro-channel.
– 𝜇 is set to 0(1) accordingly.
• Otherwise, 𝜇 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 𝜇𝑖𝑙 be the heat load partitioning factor of
grid 𝑖 on silicon layer 𝑙, 0 ≤ 𝜇𝑖𝑙 ≤ 1.
Cost assignment (cont.)
• If the hotspot exists in both side
– 𝑐𝑜𝑠𝑡(𝑖, 𝑙) = −[ 1 − 𝜇𝑖𝑙+1 𝑇𝑖𝑙+1 + 𝜇𝑖𝑙−1 𝑇𝑖𝑙−1 ]
• If the hotspot only exists in one side
– 𝑐𝑜𝑠𝑡(𝑖, 𝑙) =
− 1 − 𝜇𝑖𝑙+1 𝑇𝑖𝑙+1 , 𝑖𝑓 𝑇𝑖𝑙+1 ≥ 𝑇𝑚𝑎𝑥
−𝜇𝑖𝑙−1 𝑇𝑖𝑙−1 , 𝑖𝑓 𝑇𝑖𝑙−1 ≥ 𝑇𝑚𝑎𝑥
• If the hotspot does not exist in both side
– The node cost is assigned to a small
positive value 𝑐𝑜𝑠𝑡 𝑖, 𝑙 = 𝜖 > 0
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 microchannels.
– 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 nonhotspot 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 1.2 × 1.2𝑐𝑚2
• The grid size is 200 × 200𝜇𝑚2 (so 60 × 60
grids in each layer).
• The channel dimensions are 𝑤𝑎 =
100𝜇𝑚, 𝑤𝑏 = 400𝜇𝑚.
• The maximum temperature constraint 𝑇𝑚𝑎𝑥 =
85℃.
• 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 TSVconstrained micro-channel
infrastructure.
• Up to 87% pumping power saving
compared with the micro-channel
structure using straight channels.