An evaluation of HotSpot-3.0 block-based temperature model

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An evaluation of HotSpot-3.0 block-based
temperature model

• Damien Fetis, Pierre Michaud
• June 2006

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Temperature an important constraint
Technology Scale down
Power must be decreased to prevent temperature
from increasing
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HotSpot a thermal model for temperature-aware
microarchitecture

• http//lava.cs.virginia.edu/HotSpot/
• 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

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Outline

• Short tutorial on temperature modeling
• Short description of HotSpot block model
• Some limitations of HotSpot
• Conclusion be careful when using HotSpot

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

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Heat conduction theory
Fouriers law heat flux (W/m2) proportional to
temperature gradient
thermal conductivity
Heat equation
3D power density
heat capacity per unit volume
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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

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

• Thermal resistances ? simulate Fouriers law
• Thermal capacitances ? simulate transients
• Network consists of few layers
• horizontal resistances within layers
• vertical resistances between layers
• Single layer for the silicon die

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Compute resistance between block center and block
edge
Zsilicon die thickness
W
R
H
L
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Each block is connected to adjacent blocks
through a resistance
Thermal conductance proportional to shared edge
length
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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

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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

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Steady-state temperature
EV6 floorplan, default HotSpot configuration
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Lets take a better interface material
Interface material with 6x higher thermal
conductivity ? emphasizes horizontal heat
conduction through copper
Even the modified HotSpot is inaccurate
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Single square source

• Model the same square source with two different
  floorplans (default HotSpot parameters)
• Power 10 W

A
B
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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

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Point source transient temperature
Thermal diffusivity
opposite side starts heating
Example silicon die d0.5 mm
HotSpot miss this behavior
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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
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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 1C increase
  ?
• ? HotSpot may be wrong by orders of magnitude

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1 mm square source dissipating 10 W
Problem insufficient vertical discretization
in silicon
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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

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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 ?