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

Apr 03, 2022

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Page 1: An evaluation of HotSpot-3.0 block-based temperature model

An evaluation of HotSpot-3.0 block-based temperature model

Damien Fetis, Pierre Michaud June 2006

Page 2: An evaluation of HotSpot-3.0 block-based temperature model

2

Temperature: an important constraint

Technology Scale down

Power must be decreased to prevent temperature from increasing

Page 3: An evaluation of HotSpot-3.0 block-based temperature model

3

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

Page 4: An evaluation of HotSpot-3.0 block-based temperature model

4

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

Page 5: An evaluation of HotSpot-3.0 block-based temperature model

5

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)

Page 6: An evaluation of HotSpot-3.0 block-based temperature model

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

Page 7: An evaluation of HotSpot-3.0 block-based temperature model

7

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

Page 8: An evaluation of HotSpot-3.0 block-based temperature model

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 –  …

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

tzyxxtzyxT n

N

nnφ∑

=

=

Page 9: An evaluation of HotSpot-3.0 block-based temperature model

9

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×

=

Page 10: An evaluation of HotSpot-3.0 block-based temperature model

Silicon die Interface material

Copper heat spreader

Copper heat sink base

10

What HotSpot models

Power sources

ambient air

Page 11: An evaluation of HotSpot-3.0 block-based temperature model

11

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

Page 12: An evaluation of HotSpot-3.0 block-based temperature model

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

Page 13: An evaluation of HotSpot-3.0 block-based temperature model

13

Compute resistance between block center and block edge

R

πLZa =

W

H L

Z=silicon die thickness

πHZb =

ba

=εkHZW2

πεπλ

1+=

θπkbB 1=

bW2

⎟⎟⎟⎟

⎜⎜⎜⎜

+

+−+=

B

Bka

λτ

λλτ

εετπ )tanh(1

)tanh(11

Page 14: An evaluation of HotSpot-3.0 block-based temperature model

14

Each block is connected to adjacent blocks through a resistance

1R

2R

RRR111

21

=+

Thermal conductance proportional to shared edge length

Page 15: An evaluation of HotSpot-3.0 block-based temperature model

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

Page 16: An evaluation of HotSpot-3.0 block-based temperature model

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

Page 17: An evaluation of HotSpot-3.0 block-based temperature model

17

05

101520253035404550

Bpred IntReg IntExec

cels

ius

(rela

tive

to a

mbi

ent)

FF3DHOTSPOTHOTSPOT mod

Steady-state temperature

EV6 floorplan, default HotSpot configuration

Page 18: An evaluation of HotSpot-3.0 block-based temperature model

18

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

Page 19: An evaluation of HotSpot-3.0 block-based temperature model

19

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

Page 20: An evaluation of HotSpot-3.0 block-based temperature model

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

Page 21: An evaluation of HotSpot-3.0 block-based temperature model

21

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

Page 22: An evaluation of HotSpot-3.0 block-based temperature model

22

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

Page 23: An evaluation of HotSpot-3.0 block-based temperature model

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

Page 24: An evaluation of HotSpot-3.0 block-based temperature model

24

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

Page 25: An evaluation of HotSpot-3.0 block-based temperature model

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

Page 26: An evaluation of HotSpot-3.0 block-based temperature model

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 ?