Pulse Measurement for Thermal Impedance Characterization ...

Pulse Measurement for Thermal Impedance Characterization: HiCuM Simulation with

Recursive Electro-thermal Network

A.K. Sahoo, S. Fregonese, N. Malbert, T. Zimmer

HiCuM Workshop 2011

28 June 2011 2/21HiCuM Workshop 2011

The down scaling of electronic device dimensions is the main way to achieve better high frequency performance.

The operating quiescent point is shifted to higher current densities.

Power density of devices has increased significantly: resulting in self-heating effect in power and RF HBTs.

Thermal issue is one of the key factors limiting the performance and reliability of the devices and integrated circuits.

Systematic characterization of thermal effects inside the devices remains very important criteria to explore.

Introduction …


Self-heating effect characterization :o Pulse measurementso Low frequency S-parameter measurementso Transient electro-thermal simulation (TCAD)

Calibration and HiCuM compact model simulation

Comparison between single RTH-CTH and recursive electro-thermal network

Outline …

Part 1

Part 2 Electro-thermal scaling rule for Recursive network

Application of scaling on measurements and simulation


Pulse measurements …

Bias TEE

RF

DC + RF

RF

DC

DC

DC + RF

R = 50O

R = 50O

Bias TEE

CollectorBias

BaseBias

Base Pulse Generator

Collector Pulse Generator

DUT

P2

P1 • I = Internal resistance of pulse generator• II & IV = Coaxial cables and connectors• III = Bias TEE • V = Open capacitance of DUT

I

II III

IV V

P1/P2 P1T/P2TDUT PORT

o Experimental setup: o Passive elements :

Pulses are applied at Base and Collector terminals simultaneously and the time response of Collector currents are measured.


0.00 1.30µ 2.60µ 3.90µ 5.20µ-0.08

-0.04

0.00

0.04

0.08

P1(B

ase)

, P2(

Col

lect

or) P

ulse

(V)

I C (A

)

Time (Sec)

0

1

2

3

4

5

Measurements with optimized condition …

The transient variation of current is due to self-heating effect

Collector Pulse : 5000ns, 1.5 VBase Pulse : 3000ns, 0.95 V

DUT Technology STMicroelectronics BiCMOS9MWGeometry of Emitter window LE x WE = 10 x 0.27Device configuration CBE


HiCuM

Model of CoaxialCable-Connector


Model of BiasNetwork

Model of BiasNetwork


T

C

B


P1

P2

E

Pdiss

T

Tground

RTHCTH

HiCuM compact model simulation…

T

Pdiss

Tground

R Kr R Krn R

Kcn CKc CC

Compact model parameter from XMOD Technology


T

Pdiss

Tground

R Kr R Krn R

Kcn CKc CC

1( )( )

( ) ( )v

R z z zkA z

C z z C A z z

Δ = Δ

Δ = Δ

Kr (<1) and Kc (>1)

Thermal resistance and capacitance of an elementary volume element at a distance z from heat source with thickness Δz is characterized by C(z)Δz and R(z)Δz as :

z

??

Deep Trench

Shallow TrenchEmitter Window

Collector Contact

dz

Recursive Electro-thermal network…

28 June 2011 8/21HiCuM Workshop 2011Recursive network provides the best accuracy in time domain

Calibration and Electro-thermal modeling …

HiCuM Compact Model

Electro-Thermal Network

Single RTH-CTH

RTH

CTH

Recursive Network

Passive Elements

Pulse Generator internal resistance

Cables + connectors + Device Open Capacitance

Bias Network

0.0 1.0µ 2.0µ 3.0µ 4.0µ 5.0µ 6.0µ

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

Time (Sec)

I C (A

)

Pulse Measurements

0.0 1.0µ 2.0µ 3.0µ 4.0µ 5.0µ 6.0µ

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

Time (Sec)

I C (A

)

Pulse Measurements

0.0 1.0µ 2.0µ 3.0µ 4.0µ 5.0µ 6.0µ

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

Time (Sec)

I C (A

)

Pulse Measurements

0.0 1.0µ 2.0µ 3.0µ 4.0µ 5.0µ 6.0µ

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

Time (Sec)

I C (A

)

Pulse Measurements

0.0 1.0µ 2.0µ 3.0µ 4.0µ 5.0µ 6.0µ

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

Time (Sec)

I C (A

)

Pulse Measurements

0.0 1.0µ 2.0µ 3.0µ 4.0µ 5.0µ 6.0µ

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

Time (Sec)

I C (A

)

Pulse Measurements

10-7 10-6

0.00

0.02

0.04

0.06

0.08

Time (Sec)

I c (Am

p) Pulse Measurements

Extracted with : Single R-C Network Recrusive Network


Low frequency S-parameter measurement and thermal modeling


Low frequency S-parameter measurements :• 30 kHz – 3 GHz, •VCE = 1.5 V, 1.5 V , VBE = 0.95 V

DUT : L*W = 10*0.27 µm2

104 105 106 107 108 109

1E-4

1E-3

0.01

Frequency (Hz)

Mag

nitu

de (y

12)

MeasuredExtracted with:

Recursive Network Single RC

Low frequency S-parameter measurement and thermal modeling …

104 105 106 107 108 109

1E-4

1E-3

Frequency (Hz)

Mag

nitu

de (y

12)

VCE=1.0 V, VBE=0.95 V VCE=1.5 V, VBE=0.95 V

VCE

Thermal modeling with Single R-C and Recursive electro-thermal network.


Transient electro-thermal simulation


3D electro-thermal transient simulation with TCAD

Taking only lower part of the device including Deep Trench, Shallow Trenchand Thick SiO2 Layer

Transient electro-thermal simulation …

0.00 1.50µ 3.00µ 4.50µ 6.00µ0

5

10

15

20

25

Pow

er (W

att)

Cha

nge

in T

empe

ratu

re (K

)

Time (Sec)

0.00

0.02

0.04

0.06


1E-7 1E-6-5.0

0.0

5.0

10.0

15.0

20.0

25.0

Numerical Simulation (TCAD)Extracted with -

Single R-C Network Recrusive Network

Power

Pow

er (W

)

Incr

ease

in T

empe

ratu

re (K

)

Time (Sec)

0.00

0.02

0.04

0.06

0.08

0.10

A pulse of electric power is applied and the transient variation of device temperature has been obtained

The transient temperature variation has been modeled with electro-thermal network

Transient electro-thermal simulation and thermal modeling…


The higher value of RTH and the lower value of CTH extracted from numerical simulation can be caused by thermal flux through metal contacts that has not been taken into account.

3 6 9 12 15

1E-11

1E-10

CTH

(Ws/

K)

Emitter Length (μm)

Pulse Measurements Low Frequency S-Parameters

Measurements Numerical Simulations

4 6 8 10 12 14

1500

3000

4500

6000

7500

Emitter Length (μm)

RTH

(K/W

)

Numerical Simulations Pulse Measurements DC Measurements

Parameter extraction for single RTH – CTH network …


1 2 3 4 5 6 7 8 9

100

1000

10000

kn rR (

K/W

)

n (number of R-C cell)

Extracted from: Low Frequency S-Parameter Measurements Pulse measurements Transient Simulation

1 2 3 4 5 6 7 8 91E-12

1E-11

1E-10

1E-9

1E-8

1E-7

kn cC (W

s/K

)

n (number of R-C cell)

Extracted from: Low Frequency S-Parameter Measurements Pulse measurements Transient Simulation

LEmitterLEmitter

The overall thermal resistance, RTH = Σ R * kri, where i=0, 1, 2,.. n

T

Pdiss

Tground

R Kr R Krn R

Kcn CKc CC

The resistance and capacitance element of recursive network

Parameter extraction for recursive network …


Transient Electro-thermal Scaling rule …


Recursive network scaling …

Z tan?+Wemitter/2 Z tan?+Lemitter/2

Z

??

Deep Trench

Shallow TrenchEmitter Window

Collector Contact

( ) ( 2 tan ) ( 2 tan )( ) ( ) , 2tan , 2tan

E E

E E

A z L z W zL aZ W bZ where a b

θ φθ φ

= + ⋅ += + ⋅ + = =

11 1( ) ln

( ) ( )

NN

N N

zzE

E E Ez z

az LdzR z dzA z aW bL bz Wκ κ

++ ⎛ ⎞+

= = ⋅ ⎜ ⎟− +⎝ ⎠∫ ∫

( )( )1

1

( )23 2

( )2

( ) ( )

2 3 66

N N

N N

p

z z

pE E E E z z

C z dz C A z dz

Cabz aW bL z L W z

ρ

ρ+

−

+

+

=

= + + +

∫ ∫

zN -1 zNzm in

T

1

2NNz z ++⎛ ⎞

⎜ ⎟⎝ ⎠

1

2NNz z− +⎛ ⎞

⎜ ⎟⎝ ⎠

zN +1

min exp( )Z Z Nβ=


10-8 10-7 10-6 10-5

0

5

10

15

Frequency (Hz)

10-8 10-7 10-6 10-5

0

20

40

ΔT (K

)

ΔT (K

)

Scaling Rule Transient Temperature (TCAD Simulation)…

LE

WE

Symbols TCAD simulation Lines Extracted with scalable electro-thermal network


105 106 107 108 109

100

1000

Mag

nitu

de (Z

TH)

Frequency (Hz)

105 106 107 108 109100

1000

10000

Mag

nitu

de (Z

TH)

Scaling Rule Thermal Impedance (TCAD Simulation)…

LE

WE

Symbols TCAD simulation Lines Extracted with scalable electro-thermal network


105 106 107 108 109

1E-4

1E-3

Mag

nitu

de(Y

12)

Frequency (Hz)

105 106 107 108 109

1E-5

1E-4

WE= 0.27μm, 0.54μm

0.84μm, 1.08μm

LE= 3μm, 5μm

10μm, 15μm

Mag

nitu

de(Y

12)

105 106 107 108 109-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

Phas

e(Y

12) (

degr

ee)

Frequency (Hz)

105 106 107 108 109-2.0

-1.5

-1.0

-0.5

0.0

WE= 0.27μm, 0.54μm

0.84μm, 1.08μm

LE= 3μm, 5μm

10μm, 15μm

Phas

e(Y

12) (

degr

ee)

Scaling Rule Thermal modeling of Y-parameter…

LELE

WEWE

Symbols MeasurementsLines Compact model simulation with scalable electro-thermal network

DUT Technology STMicroelectronics BiCMOS9MWDevice configuration CBEBC


The transient electro-thermal effect has been characterized with pulse measurements and verified through S-Parameter measurements and transient simulations.

The extraction of CTH parameter for small device dimension can be achieved by employing a complete calibration.

Two different electro-thermal networks have been compared to demonstrate time domain thermal spreading impedance.

The scaling behavior of transient electro-thermal phenomena has been investigated and verified through measurements and simulations.

Thank you

Conclusions …

Pulse Measurement for Thermal Impedance Characterization ...

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