1 An Improved Block-Based Thermal Model in HotSpot 4.0 with Granularity Considerations Wei Huang 1, Karthik Sankaranarayanan 1, Robert Ribando 3, Mircea Stan 2 and Kevin Skadron 1 Departments of 1 Computer Science, 2 Electrical and Computer Engineering and 3 Mechanical and Aerospace Engineering, University of Virginia

2 Hi! I’m HotSpot  Temperature is a primary design constraint today  HotSpot – an efficient, easy-to-use, microarchitectural thermal model  Validated against measurements from Two finite-element solvers [ISCA03, WDDD07] A test chip with a regular grid of power dissipators [DAC04] A Field-Programmable Gate Array [ICCD05]  Freely downloadable from

3 A little bit of History  Version 1.0 – a block-based model  Version 2.0 – TIM added, better heat spreader modeling  Version 3.0 – grid-based model added  Version 4.0 coming soon!

4 Why this work?  Michaud et. al. [WDDD06] raised certain accuracy concerns  A few of those had already been addressed pro-actively with the grid- based model  This work tries to address the remaining and does more  Improves HotSpot to Version 4.0 – downloadable soon!

5 Outline  Background  Overview of HotSpot  Accuracy Concerns  Modifications to HotSpot  Results  Analysis of granularity  Conclusion

6 Outline  Background  Overview of HotSpot  Accuracy Concerns  Modifications to HotSpot  Results  Analysis of granularity  Conclusion

7 Overview of HotSpot  Similarity between thermal and electrical physical equations  HotSpot discretizes and lumps ‘electrical analogues’ (thermal R’s for steady-state and C’s for transient)  Lumping done at two levels of granularity Functional unit-based ‘block-model’ Regular mesh-based ‘grid-model’  Thermal circuits formed based on floorplan  Temperature computation by standard circuit solving Analogy between thermal and electrical conduction

8 Structure of the `block-model’ Sample thermal circuit for a silicon die with 3 blocks, TIM, heat spreader and heat sink (heat sources at the silicon layer are not shown for clarity)

9 Outline  Background  Overview of HotSpot  Accuracy Concerns  Modifications to HotSpot  Results  Analysis of granularity  Conclusion

10 Accuracy concerns from [WDDD06]  Spatial discretization – partly addressed with the `grid-model’ since version 3.0 For the same power map, temperature varies with floorplan Floorplans with larger no. of blocks better Floorplans with high-aspect-ratio blocks inaccurate  Transient response Slope underestimated for small times Amplitude underestimated

11 Other issues and limitations  Forced isotherm at the surface of the heat sink  Temperature dependence of material properties – not part of this work

12 Outline  Background  Overview of HotSpot  Accuracy Concerns  Modifications to HotSpot  Results  Analysis of granularity  Conclusion

13 Block sub-division Version 3.1 – a block is represented by a single node Version 4.0 – sub-blocks with aspect ratio close to 1

14 Heat sink boundary condition Version 3.1 – single convection resistance, isothermal surface Version 4.0 – parallel convection resistances, center modeled at the same level of detail as silicon

15 Other modifications  Spreading R and C approximation formulas replaced with simple expressions (R = 1/k x t/A, C = 1/k x t x A)  Distributed vs. lumped capacitance scaling factor – 0.5  ‘grid-model’ enhancements – apart from the above: First-order solver upgraded to fourth-order Runge-Kutta Performance optimization of the steady-state solver

16 Outline  Background  Overview of HotSpot  Accuracy Concerns  Modifications to HotSpot  Results  Analysis of granularity  Conclusion

17 Experiment 1 – EV6-like floorplan

18 Results with good TIM ( k TIM = 7.5W/(m-K) )

19 Results with worse TIM ( k TIM = 1.33W/(m-K) )

20 Transient response – bpred Transient response for different power pulse widths applied to the branch predictor. Power density is 2W/mm 2 ( k TIM = 7.5W/(m-K) ). Other blocks have zero power dissipation.

21 Experiment 2 – 1 mm 2 square heat source Version 3.1Version 4.0

22 Results Center temperature for different heat source sizes with a power density of 1.66W/mm 2 – (a) with good TIM ( k TIM = 7.5W/(m-K) ) (b) with worse TIM ( k TIM = 1.33W/(m-K) )

23 Transient response: high power density, worse TIM Transient temperature response for 1mm x 1mm source with 10Watts with worse TIM material (k TIM = 1.33W/(m-K)).

24 Outline  Background  Overview of HotSpot  Accuracy Concerns  Modifications to HotSpot  Results  Analysis of granularity  Conclusion

25 Spatial filtering  The Norton equivalent first-order thermal spatial RC circuit  Low-pass filter in the spatial domain  Blocks with high power density need not be hot spots (when small enough)

26 Spatial filtering – continued...  Thermal RC is distributed  First-order approximation not sufficient  3-ladder RC (similar to HotSpot) approximates well Comparison of 3-ladder thermal spatial RC model and ANSYS simulation for different heat source sizes.

27 Outline  Background  Overview of HotSpot  Accuracy Concerns  Modifications to HotSpot  Results  Analysis of granularity  Conclusion

28 Summary, limitations and caveats  This work acknowledges and addresses the concerns in [WDDD06]  `grid-model’ [DAC04] had addressed part of the discretization aspect earlier  HotSpot 4.0 addresses remaining and does more  Careful use of vertical layers necessary, material properties’ dependence on T not modeled  Soon to be available at

29 Questions?

30 Backup – ATMI [MoBS07]  Analytical model, has good accuracy  A diversity in modeling is good for the community  Vis-a-vis HotSpot – advantages Immune to spatial discretization  Disadvantages Less flexibility (esp. in vertical layers) Computationally intensive (esp. when looking for temperature with a particular property)

31 Backup – Transient response: high power density, good TIM Transient temperature response for 1mm x 1mm source with 10Watts power and a good TIM (k TIM = 7.5W/(m-K)).

32 Backup – Transient response: low power density, good TIM Transient temperature response for a 7mm x 7mm source with 10Watts power and a good TIM (k TIM = 7.5W/(m-K)).

33 Backup – Granularity (1)  A first-order electrical RC circuit

34 Backup – Granularity (2)  The Thevenin equivalent first-order thermal spatial “RC” circuit.