Thermal Model of a Thinned-Die Cooling System

N. Boiadjieva … NPTest, Inc

P. Koev… MIT, Dept. of Mathematics

Outline

• Optical Probing and Cooling

• Problem Statement

• System Characterization

• Mathematical Model Development

• Conclusions

Optical Probing & Cooling

Socket & Clamp

Cooling system

Load Board

Die

Carrier

Tapered Final Lens ElementTransparent

Diamond Window (Heat Sink)

DetectorDetector

Stimulus

Optical Probing

Cooling System setup

DUT

Heat Exchanger

Heat Spreader, Diamond window

Clamp

Lens

Cooling System X-Section

Transparent Diamond k=1800 W/m-K

Device clamp

Thermocouple, TB

Thermocouple, THS

LensCopper

k=374 W/m-K

Thermal System Characterization

TDUT=f(Wattage, air Flow rate, cooling air TAIR)

Heat Spreader

Thermocouple, TDIA

during characterization only

Diamond window

Thermocouple, TB

Heat Exchanger

Thermocouple, THS

DUT

Center line

Package

Heat Exchanger

Cooling air, TAIR

Flow rate

Problem Statement

Develop a mathematical model so that both device temperature and device power could be derived through the analytical expression.

TDUT

TB

THS

TAIR

Flow rate

• TDUT=f1(Wattage, TAIR, FLOW, THS)• Wattage=f2(THS,TAIR, FLOW)

Thermal System Characterization

TDIA

TB

THS

TAIR

Air Flow rate

Mathematical model development

Thermocouple, TDIA

Diamond window

Thermocouple, TB

Cooling air, TAIR

Thermocouple, THS

DUT

x

TDUT THS TB TAIR

TDIA~TDUT, .026KΔT

Mathematical model … cont’d

x

TDUT THS TB TAIR

3D case 1D non uniform rod

In Steady State 1D Heat equation

Uniform rod

0]dx

du[K(x)

dx

d

UNKNOWN

Xat ty ConductiviHeat K(x)

0dx

ud2

2

etemperaturtxu ),(

Non uniform rodNon uniform rod

Mathematical model … cont’d

x

TDUT THS TAIR

l1 l2

SolutionSolution

Uniform rodAIR

21

2DUT

21

1HS T

ll

lT

ll

lT

baxu(x)

AIRDUTHS a)T(1aTT Non uniform rod

Non uniform rod…cont’d

x

TDUT THS

TAIRTFP

Flow

FPDUTHS a)T(1aTT

TFP=f (TAIR, Flow)Need to define

measure ???

TFP=f (TAIR, FLOW)

x

TDUT THS

TAIR

cTFP

d

FLOW-h3FP beTT

TFP TAIR

T3

T3

mt3FP beTT

FLOW

1t

skW FLOW-h

FP beskWT

Final Formula(s)

FPDUTHS a)T(1aTT

measure

???FLOW-h

FP beskWT

)e(1

}]e 17.38)(T1.44{13.78T 1.49T [2.93W

FLOW2

FLOW2AIRHSB

]13.78)e0.69W(T13.781.03[0.69W2.03TT FLOW2AIRHSDUT

TDUT

TB

THS

TAIR

Flow rate

Results Comparison

TDUT

TB

THS

TAIR

Flow rate,

Error was less that 10% over the entire temperature and power range

Conclusions

• Cooling system for thinned 150W microprocessor - characterized

• 3-D Heat Transfer simplified to a 1-D non uniform rod case

• Device temperature and input power can be determined through an analytical expression

• Future software control capabilities.