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

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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

1.  Short tutorial on temperature modeling 2.  Short description of HotSpot block model 3.  Some limitations of HotSpot

Conclusion: be careful when using HotSpot

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Processor temperature model

Material characteristics, heat-sink thermal resistance, etc…

Power-density map q(x,y,t)

Temperature model

Ambient temperature

processor temperature

T(x,y,t)

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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

Tkq ∇−=Fourier’s law: heat flux (W/m2)

proportional to temperature gradient

thermal conductivity

tTCqg∂

∂=⋅∇−

Heat equation

heat capacity per unit volume

3D power density

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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 –  …

),,,(),,,('0

tzyxxtzyxT n

N

nnφ∑

=

=

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1D thermal resistance

Thermally-insulated side

Uniform power P over area A

L

•  Right cylinder –  Length = L –  Cross section area = A –  Thermal conductivity = k

T1

T2

LTTk

AP 21 −=

Uniform power over cross section

uniform temperature over cross section

PRTT ×=− 21

Define thermal “resistance” AkLR×

=

Silicon die Interface material

Copper heat spreader

Copper heat sink base

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What HotSpot models

Power sources

ambient air

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How HotSpot “solves” the heat equation

Model power generation as current sources

Model ambient as ground

Thermal resistances

Instead of using formal methods, solve an “electrical” network

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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

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Compute resistance between block center and block edge

R

πLZa =

W

H L

Z=silicon die thickness

πHZb =

ba

=εkHZW2

=θ

πεπλ

1+=

θπkbB 1=

bW2

=τ

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

+

+−+=

B

Bka

Rλ

λτ

λλτ

εετπ )tanh(1

)tanh(11

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Each block is connected to adjacent blocks through a resistance

1R

2R

RRR111

21

=+

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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05

101520253035404550

Bpred IntReg IntExec

cels

ius

(rela

tive

to a

mbi

ent)

FF3DHOTSPOTHOTSPOT mod

Steady-state temperature

EV6 floorplan, default HotSpot configuration

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Let’s take a better interface material

0

5

10

15

20

25

30

35

Bpred IntReg IntExec

cels

ius

(rela

tive

to a

mbi

ent)

FF3DHOTSPOTHOTSPOT mod

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

A

B

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

•  Power = 10 W

mm 21

0

50

100

150

200

250

0.001 0.003 0.005source side (meters)

cels

ius

(rel

ativ

e to

am

bien

t)

ff3dHotSpot AHotSpot BHotSpot mod AHotSpot mod 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

α4

2dt =

d

0=t

opposite side starts heating

)4

erfc(2

),(t

rkrPtru

απ=

Ck

=αThermal diffusivity

Example: silicon die

d=0.5 mm

sm / 10.7 25−≈α

s 9004

2

µα≈

d HotSpot miss this behavior

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Volume vs. surface power sources

Sources spread in bulk silicon Sources concentrated in thin layer

time t

temperature

time t

temperature

t~ 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 1°C increase ?

•  HotSpot may be wrong by orders of magnitude

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1 mm square source dissipating 10 W

0

5

10

15

20

25

30

0 0.0002 0.0004 0.0006 0.0008 0.001

seconds

cels

ius

(rela

tive

to a

mbi

ent)

HotSpot AHotSpot BFF3D

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 ?