thermal modeling of fluid cooled 3d ics
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Thermal Modeling of Fluid Cooled 3D ICs
Ayman Dorrah, Jeff Nicholls and Miaofei Mei
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• Introduction/ Motivation
• Architecture
• Thermal Model
• Modeling of Solids
• Modeling of Fluids
• Solution Procedure
• Results
• Example results
• Comparison between BE and TR methods
• Conclusion
• References
Agenda:
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• There is demand for ever increasing powerful integrated circuits, but interconnecting
the components on a 2D chip has poor scalability, so the semiconductor industry is
moving towards 3D IC stacks.
• One of the challenges of engineering 3D ICs is designing for heat dissipation.
• Heat sinks are incapable of cooling the middle of a stack.
• Liquid coolant flowing through microchannels in between the layers of ICs is a
scalable solution for the heat problem.
• A thermal model of the 3D IC stack and microchannel system is presented.
Introduction/ Motivation:
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• A compact model based on the work of Sridhar et al.
• Spatial dimensions are coarsely discretized, leading to large speedups. Time is
discretized through finite differencing.
• The model is solved using Backward Euler and Trapezoidal Rule methods.
Architecture:
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Thermal Modeling of solids: Conservation Law
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Thermal Modeling of Solids: Equivalent Circuit
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Thermal Modeling of Fluids: Conservation Law
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Thermal Modeling of Fluids: Equivalent Circuit
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Thermal Modeling of Fluids:
• Boundary Conditions Dirichlet BCs at Channel’s Inlet and Neumann BCs
everywhere else.
• C is a diagonal matrix and G is an asymmetric block-tridiagonalmatrix
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• Input stack file (.stk) -> equivalent circuit -> G, C, B
• Solution computed using Backward Euler:
• ..and Trapezoidal Rule:
• With 400,000 nodes, 600 timesteps, solution takes ~ 7 mins
Solution Procedure (Solver):
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TR Ringing
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• Try to solve:
• Exact solution for nth time step:
• Numerical solution:
• For :
Numerical solution approaches zero but flips between positive and negative.
TR Ringing: Stability Analysis
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• Smoothing attempts to correct ringing:
While (smoothing):
Calculate xn+1
Generate improved estimate for xn
Use improved estimate to recalculate xn+1
• Repeated for multiple timesteps after a change in the input
Smoothing
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Smoothing
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Example Results
• The test case is composed of the layers
(7 mm long by 10 mm wide)
• Initial temperature was 20 ◦C. The
active silicon was producing heat at a
constant 50 W/cm2. A hotspot produced
between at 50 W/cm2, 250 W/cm2 and
450 W/cm2 of heat. The microchannels
were 50 µm wide by 100 µm tall. The
incoming coolant was 26 ◦C. Coolant
velocities of 1.62 m/s, 0.81 m/s, and
0.405 m/s were simulated.
• The test case was simulated until t = 0.6
s with both BE and smoothed TR using a
timestep of Δt = 0.001 s.
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Example Results
• Temperature over time in the middle of the die:
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Example Results
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Example Results
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Example Results
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Results: Comparison Between BE and TR methods
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Results: Comparison Between BE and TR methods
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Results: Comparison Between BE and TR methods
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• Presented a compact model capable of efficiently simulating thermal effects in 3D
microchannel cooled ICs
• Model demonstrates/extends the applicability of the equivalent circuit approach
• Trapezoidal Rule suffers from “ringing” in simulations with fast transients
• Smoothed Trapezoidal Rule is a good way of reducing ringing and improving
simulation accuracy with minimal time overhead
Conclusion:
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References:
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