1. An evaluation of HotSpot-3.0 block-based temperature model
Damien Fetis, Pierre Michaud
June 2006

2. Temperature: an important constraint
Technology Scale down
Power must be decreased to prevent temperature from increasing

3. HotSpot: a thermal model for temperature-aware microarchitecture
Based on thermal resistances and capacitances
It is becoming a standard tool in the computer architecture community
Several tens of works based on HotSpot have been published so far

4. Outline Short tutorial on temperature modeling
Short description of HotSpot block model
Some limitations of HotSpot
Conclusion: be careful when using HotSpot

5. Processor temperature model
Power-density map q(x,y,t)
Material characteristics, heat-sink thermal resistance, etc…
processor temperature T(x,y,t)
Temperature model
Ambient temperature

6. Qualitative accuracy Accurate temperature number ?  forget it !
If the conclusions of your research depend on precise parameter values, what you are proposing probably has little value
What we need for research: qualitative accuracy
Model can tell whether an idea is worth or not
We would like to be consistent with physics

7. Heat conduction theory
Fourier’s law: heat flux (W/m2) proportional to temperature gradient
thermal conductivity
Heat equation
3D power density
heat capacity per unit volume

8. Solving the heat equation
Analytical method
Exact solution
Possible only for simple geometries
Finite methods
Search (xn) that makes T’ “close” to the actual solution
 solve a system of equations
Finite differences
Finite elements
Spectral methods …

9. 1D thermal resistance Right cylinder Length = L Cross section area = A
Thermal conductivity = k
Uniform power over cross section
 uniform temperature over cross section
Thermally-insulated side T2 L T1
Uniform power P over area A
Define thermal “resistance”

10. What HotSpot models ambient air Copper heat sink base
Copper heat spreader
Interface material
Silicon die
Power sources

11. How HotSpot “solves” the heat equation
Model ambient as ground
Instead of using formal methods, solve an “electrical” network
Thermal resistances
Model power generation as current sources

12. HotSpot block model Thermal “resistances”  simulate Fourier’s law
Thermal “capacitances”  simulate transients
Network consists of few layers
“horizontal” resistances within layers
“vertical” resistances between layers
Single layer for the silicon die

13. Compute resistance between block center and block edge
Z=silicon die thickness W R H L

14. Each block is connected to adjacent blocks through a resistance
Thermal conductance proportional to shared edge length

15. HotSpot is empirical Not based on mathematical foundations
Resistance formula applied without justification
Was derived for definite boundary conditions that do not apply here
Coarse “vertical” space discretization
Problem with empirical models: more difficult to validate
Require extensive validation
Not sufficient to validate a few points in the parameter space
Error may vary significantly with parameter values

16. Evaluation We are not validating HotSpot
We are just highlighting some of its limitations
 deliberate focus on problematic cases
Compare HotSpot block model with finite-element solver FF3D
Model same physical system as HotSpot
Two versions of HotSpot
The original one
Our modified version with simple 1D resistance formula

17. Steady-state temperature
EV6 floorplan, default HotSpot configuration

18. Let’s take a better interface material
Interface material with ~6x higher thermal conductivity
 emphasizes “horizontal” heat conduction through copper
Even the modified HotSpot is inaccurate

19. Single square source
Model the same square source with two different floorplans (default HotSpot parameters)
Power = 10 W A B

20. What do we learn ?
In some cases, HotSpot may be significantly inaccurate
The usefulness of the complicated thermal resistance formula is not obvious
HotSpot documentation indicates that mixing small and large blocks may be source of inaccuracy  we confirm

21. Point source: transient temperature
Thermal diffusivity
opposite side starts heating
Example: silicon die
d=0.5 mm
HotSpot miss this behavior

22. Volume vs. surface power sources
Sources spread in bulk silicon
Sources concentrated in thin layer
temperature
temperature
time t
time t
HotSpot behavior
Close to actual behavior

23. What this implies for HotSpot
HotSpot block-model considers a single network layer for the silicon die
 cannot produce correct behavior for small times
 Underestimates slope of temperature transient
E.g., how long does it take to get a 1°C increase ?
 HotSpot may be wrong by orders of magnitude

24. Problem: insufficient “vertical” discretization in silicon
1 mm square source dissipating 10 W
Problem: insufficient “vertical” discretization in silicon

25. Conclusion Be careful when using HotSpot
Good to read a little heat conduction theory before …
Heat conduction ≠ electric conduction
Ok to use HotSpot for confirming a priori intuitions
Draw qualitative conclusions, not quantitative ones
In case of doubt, check with formal methods that HotSpot is correctly calibrated for a particular use

26. HotSpot still evolving
This study was only for HotSpot block model
Version 3.0 features a new grid mode
Discretization is automatic (but “vertically”)
Permits defining multiple silicon layers
 must be validated
HotSpot will probably continue to evolve
Will end up resembling finite differences ?