april 8, 2005mos-ak, strasbourg self-heating investigation of bulk and soi transistors pierre-yvan...

April 8, 2005 MOS-AK, Strasbourg

Self-heating investigation of bulk and SOI transistors

Pierre-Yvan Sulima, Hélène Beckrich, Jean Luc Battaglia, Thomas Zimmer

University of Bordeaux 1, France

ST Microelectronics

April 8, 2005 MOS-AK, Strasbourg 2/32

Preface

This presentation deals • with bipolar transistors

• with heat transfer

• but: Heat transfer is material dependant

• MOS & BJT => Si

• Results are valid for MOS, too ? So, this presentation may interest you


Outline

Introduction: self-heating Measurement set-up Self-heating modelling Equivalent networks Predictive model Results, conclusion and perspectives


Introduction: macroscopic

Self-heating: • Heating of the device due to its power

dissipation

Bipolar transistor:

• P = IC VCE + IB VBE

• T = P ZTH


Introduction: impact

Electrical Power T changes Temperature variation

• Mobility variation

• E-gap variation

• IC, IB variation

• Electrical power variation Feedback: convergence problems for

electrical and physical simulators Limit of operation in high power region


Measurement set-up: step 1

Bipolar transistor

Ib

T Vce

Oscillo.

0.0

0.5

1.0

1.5

2.0

2.5

-10 0 10 20 30 40 50

t (µs)

Vce

(V)

0.915

0.920

0.925

0.930

0.935

0.940

0.945

-5 0 5 10 15 20 25 30 35 40 45

t (µs)

Vb

e (V

)

VBE(t):

VCE(t):


Calibration: Measure VBE(T), step 2

IB = const

VCE = VCElow Variation of T

• 27°C 50°C

Measure of VBE0.915

0.920

0.925

0.930

0.935

0.940

0.945

25 30 35 40 45

T(°C)

Vbe

(V

)


Dynamic behaviour: Trise(time)

From VBE(t) And VBE(T) Trise (t)

New method which permits to take into account the temperature rise @ VCE=VCEmin => Mixdes05

0

2

4

6

8

10

12

14

16

18

20

0 5 10 15 20Time (µs)

Tris

e (K

)


Electrical modelling of Trise(t)

State of the art(VBIC, MEXTRAM, HICUM)

Results

RTH CTH

Trise

B

C

E

Pdiss

0

1

2

3

4

5

0 2 4 6 8 10Time (µs)

Trise

(K)

measuresingle exponential modeldouble exponential model

THTH

THTH CpR

RpZ

1

t

TtTrise exp1


New thermal self-heating model

The differential equation describing heat transfer is:•

: thermal conductivity, [W/m°C]

• c: specific heat, [J/kg°C]: material density, [kg/m3]

• T: temperature, [°C] /c: thermal diffusivity, [m2/s]

t

TcT


Geometric presentation

0 L

x

y

z

W

heat source

q (r,t)

r

z

r0

Transistor, HBT

Schematic system representation with Cartesian co-ordinates

Schematic system representation with cylindrical co-ordinates: bidimensional axisymmetric geometry

t

T

az

T

r

T

rr

T

11

2

2

2

2

t

TcT

WL

r0


Boundary & initial conditions

q (r,t)

r

z

r0

Initial condition: t=0,

0,0

rforr

T

zrforTT ,,

00,0),( rrzfortrqz

T

0,00 rrzforz

T

TT


Analytical problem resolution

Calculation of the thermal impedance Trise(t) = Pdiss(t) ZTH(t) Transform into the Laplace domain and

solution of differential equation: pCR

R

RZ

pZTHTH

TH

THeq

TH

1111

)( q0Zeq

Rth

0


Comparison

Standard• Thermal impedance:

• Step response:

New model• Thermal impedance:

• Step response:

THTH

THTH CpR

RpZ

1

t

TtTrise exp1

B

terfc

B

texp1A)t(T

2rise

pCR

R

RZ

pZTHTH

TH

THeq

TH

1111

)(


Results (1)

Comparison between the standard (double exponential) and new model• a 1E2B2C 0.5x10 µm device

0

1

2

3

4

5

0 2 4 6 8 10

Time (µs)

Trise

(K)

measure

double exponential model

new model


Results (2)

0

2

4

6

8

10

12

14

16

18

20

0 5 10 15 20Time (µs)

Tri

se (

K)

measure

new model

IB = 150µA

IB = 50µA

Measurement for different Ib currents @ different power dissipation

• a 1E1B1C 0.8x6.4 µm device


Equivalent networks

Electrical-thermal networks for SPICE simulation

• Represent the thermal impedance as accurate as possible

• Have as few parameters as possible

• The parameters have a physical meaning

pCR

RpZ

THTH

THTH

1

)(


Equivalent network recursive parallel

Recursive parallel network

RTHPdiss

Tel

C

R

kC

kR

Ki-1C

Ki-1R

k2C

k2R

Ztrans


Results:recursive parallel

Recursive parallel network • N=10

• RTH, R, C, k

4 parameters have to be determined

Independent of cell number

1

10

100

1000

10000

1.0E+00 1.0E+02 1.0E+04 1.0E+06 1.0E+08 1.0E+10 1.0E+12

Frequency (Hz)

ZT

H (

K/W

)

Analytical model

Parallel recursive network

-50

-40

-30

-20

-10

0

1.0E+00 1.0E+02 1.0E+04 1.0E+06 1.0E+08 1.0E+10 1.0E+12

Frequency (Hz)

Phas

e (°

)

Analytical model

Parallel recursive netw ork

-10dB/dec

- 45°


Time domain

Step response of the parallel recursive circuit

0

2

4

6

8

10

12

0 10 20 30 40 50Times (µs)

Tel (

°C)

Parallel recursive network

Exponential model

Measurement


Predictive Modelling

Calculate the thermal impedance as a function of the layout data• Numerical approach

• Geometrical approach


Numerical approach

HBT cross section: 3 layers: • back end (Isolation and metallization)• Active layer (intrinsic transistor + deep trench isolation)• Substrate

Resolving the Heat transfer equation with the specific initial and corner conditions

p

p SiGe

Burried layer n+

SiO2 SiO2SiO2

n+p+ p+

SIC n

BE

C

B

Substrate pp+ deep trench

Emitterpoly n+

Extrinsic basepoly p+

n épitaxial

SEG SiGe Base

Collector sinkern+

+

y

x

z

e0

e1

e2

Ф

λ2 (ρC)2

λ1

λ0

(ρC)1

(ρC)0

λe2Ф(t)

(ρC)e2

λe0

(ρC)e0

e2

z

(ρC)e1 λe1

x


Results (RTH = f(emitter area))

Physical approach Numerical calculation takes some minutes Actually: some problems with CTH scaling

RTH=f(Se)

0.00E+00

1.00E+03

2.00E+03

3.00E+03

4.00E+03

5.00E+03

6.00E+03

7.00E+03

0.00E+00 2.00E+00 4.00E+00 6.00E+00 8.00E+00

Se(µm2)

RT

H(K

/W) RTHIXLexp

RTHIXLexp2

RTHIXLnum

RTHST


Geometrical approach


RTH calculation


Results: output characteristics


HBT on SOI

Schematic Cross section TEM Cross section view


Results - Layout investigation:

Type Active surface [µm2]

# E(emitter)

Active E-surface [µm2]

RTH [K/W]

Q1 0.882 12 0.15*0.49 3100

Q2 0.8775 5 0.15*1.17 5400

Comparison to bulk Si: HBT SOI = 2 * HBT bulk (! Very rough estimation !)


Discussion Limit of the standard model Development of a new accurate model

• Resolution of heat transfer differential equation

• Physical model

Representation with equivalent networks • The parallel recursive network is very accurate

• 4 parameters needed

Use in compact circuit modelling


Under work: predictive model

Numerical approach Geometrical approach Both approaches give good results

• Calculation time

• Usability

Methods applied to HBT on SOI


Perspectives

Thermal coupling between transistors Power device modelling Layout optimisation Investigation of the thermal behaviour of MOS

transistors ? (cooperation)• Tools

• Methods

• Equations

• Extraction methods

April 8, 2005 MOS-AK, Strasbourg

Thanks for your attention

The paper is open for discussion.

april 8, 2005mos-ak, strasbourg self-heating investigation of bulk and soi transistors pierre-yvan...

Documents

v ce t

t t rise t new method

thermal impedance t

device slide

mixdes05 slide

v ce low variation of

t rise time

p diss t z th t