111 Copyright 2007, Toshiba Corporation. HiCUM Workshop 2007

Modification of HiCUM and G-P model card for DFM (Design For Manufacturing) Applications

Sadayuki Yoshitomi

Toshiba Corp, Semiconductor Company

222

Objective of this work

SPICE model (Golden Device)

MASK Design

Look-up tablePT and FT measurement data

SPICE model (new revision)

Process&PT Assembly FT

Data MiningFinding a critical factor

DOE/MonteCarloanalysis

Creation of PCM-Model

Checkfabrication history

(machine/condition)

PCM model cardReflects real-process

fluctuation Long Term JOB !

BJT Physical model cardReasonable estimation of process fluctuation.

Uses “COMMON Key Word” for process/circuit designers.

Quick ValidationReasonableEstimation.

333

Key Process variables for Bipolar Transistors’ Fabrication

N_eN_E0=3e20

N_bN_B0=8e18

N_sicN_sic=1e17

N_cN_c=1e19

EmitterA_e,N_e,W_e

Base –epi width Doping concentration / Gecomposition

Doping Concentration and Depth of in SiC region

Emitter patterning/Doping concentration

BaseN_b,W_b,d_EG,Rpinch

CollectorN_sic, W_sic

444

Structure of BJT Physical Model Card

V A RL a yo u tP a ra m s

V D C I0 =(b o l tzm a n n * 3 0 0 /q e le c tro n )* l n ( (N _ b 0 * N _ c )/N _ i * * 2 )V D C I= (b o l tzm a n n * 3 0 0 /q e l e c tro n )* l n ( (N _ b * N _ c )/N _ i * * 2 )T _ d e p c 0 =s q rt( 2 * e _ s i * V D C I0 /q e le c tro n /N _ c )T _ d e p c =s q rt( 2 * e _ s i * V D C I/q e le c tro n /N _ c )e _ s i o 2 =3 .8 5 * e 0 /1 0 0e _ s i =1 1 .7 * e 0 /1 0 0u h N C _ d e f=1 9 0 8 .8 -4 1 .8 1 * l o g 1 0 (N _ s i c 0 )

u h N E _ d e f=1 9 0 8 .8 -4 1 .8 1 * lo g (N _ e 0 )u h N B _ d e f=1 9 0 8 .8 -4 1 .8 1 * lo g (N _ b 0 )u h N E =1 9 0 8 .8 -4 1 .8 1 * lo g (N _ e )u h N B =1 9 0 8 .8 -4 1 .8 1 * lo g (N _ b )u h N C =1 9 0 8 .8 -4 1 .8 1 * lo g (N _ c )u e N B _ d e f=7 0 2 2 .7 -1 6 0 * lo g (N _ b 0 /1 .3 )u e N E _ d e f=7 0 2 2 .7 -1 6 0 * lo g (N _ e 0 /1 .3 )u e N C _ d e f=7 0 2 2 .7 -1 6 0 * lo g (N _ s i c 0 /1 .3 )u e N C =7 0 2 2 .7 -1 6 0 * lo g (N _ c /1 .3 )u e N B =7 0 2 2 .7 -1 6 0 * lo g (N _ b /1 .3 )u e N E =7 0 2 2 .7 -1 6 0 * lo g (N _ e /1 .3 )p c _ d e f=1 0 * * (-0 .6 9 9 * lo g (N _ s i c 0 )+1 1 .2 8 )p e _ d e f=1 0 * * (-0 .6 9 9 * lo g (N _ e 0 )+1 1 .2 8 )p b _ d e f=1 0 * * (-0 .6 9 9 * lo g (N _ b 0 )+1 1 .2 8 )p b =1 0 * * (-0 .6 9 9 * lo g (N _ b )+1 1 .2 8 )

p c =1 0 * * (-0 .6 9 9 * lo g (N _ c )+1 1 .2 8 )p e =1 0 * * (-0 .6 9 9 * lo g (N _ e )+1 1 .2 8 )N _ b u ri e d =3 .0 e 1 9N _ s i c 0 =1 .0 e 1 7N _ b 0 =8 e 1 8N _ s u b =1 e 1 5N _ e 0 =3 .0 e 2 0D _ h = (b o l tzm a n n * 3 0 0 /q e l e c tro n )* u h N BD _ e 0 =(4 6 8 8 0 0 0 )* N _ b 0 ^(-0 .3 2 2 )D _ e = (4 6 8 8 0 0 0 )* N _ b ^(-0 .3 2 2 )m =2 .0N _ e =N _ e 0N _ c =N _ s i c 0N _ b _ te s t=1 e 2 0 s ta t{ g a u s s + /- 1 5 % }N _ i=1 4 5 0 0 0 0 0 0 0 0

E qnV ar

V A RFlu c tu a ti o n _ R a ti o _ fo r_ H iC U M

K _ th c s =(W _ c /u e N C )* (u e N C _ d e f/W _ c _ s i c )* ( (0 .5 * W _ c +W _ b )/(0 .5 * W _ c _ s i c +W _ b 0 ) )K _ V p t= (N _ c /N _ s i c 0 )* (W _ c /W _ c _ s i c )* * 2K _ te f0 =(1 /K _ h fe )* (W _ e /W _ e 0 )* * 2 * (u h N E /u h N E _ d e f)K _ fth c =(W _ c /W _ c _ s i c )* ( (W _ c _ s i c +2 * W _ b 0 )/(W _ c +2 * W _ b ) )

K _ tb fvs = ( (W _ b * W _ c )/(W _ b 0 * W _ c _ s i c ) )* (u e N C _ d e f/u e N C )K _ R C I=(p c /p c _ d e f)* ( (W _ c -T _ d e p c ) / (W _ c -T _ d e p c 0 ) )K _ C J C I0 =s q rt(N _ b /N _ b 0 /K _ V D C I0 )K _ C J E I0 =s q rt(N _ b /N _ b 0 /K _ V D E I0 )K _ V D C I0 = ln ( (N _ c * N _ b )/N _ i * * 2 ) / l n ( (N _ s i c 0 * N _ b 0 )/N _ i * * 2 )K _ V D E I0 = ln ( (N _ e * N _ b )/N _ i * * 2 ) / l n ( (N _ e * N _ b 0 )/N _ i * * 2 )K _ rb x=(p b /W _ b )/(p b _ d e f/W _ b 0 )K _ rb i0 =(p b /W _ b )* (W _ b 0 /p b _ d e f)K _ ta u f0 =( W _ b * * 2 * D _ e ^(-1 ) )/( W _ b 0 * * 2 * D _ e 0 ^(-1 ) )K _ q p 0 =(u e N B _ d e f* W _ b * N _ b )/(u e N B _ d e f* W _ b 0 * N _ b 0 )K _ h fc = (u e N B * N _ b * * 2 )/(u e N B _ d e f* N _ b 0 * * 2 )K _ h fe = (u e N B * N _ b * * 2 )/(u e N B _ d e f* N _ b 0 * * 2 )K _ h je i =K _ C J E I0 * (N _ b * W _ b )/(N _ b 0 * W _ b 0 )K _ h j c i =e xp ( (1 /2 6 e -3 )* (W _ b 0 -W _ b ) )K _ c 1 0 =(u e N B * N _ b * * 2 )/(u e N B _ d e f* N _ b 0 * * 2 )

E qnV ar

V A RGe o m e tryP a ra m s 1

W _ e =W _ e 0W _ e 0 =3 .0 uW _ b 0 =7 .0 uW _ c _ s i c =1 4 5 uW _ c =W _ c _ s i c

E qnV ar

V A RGe o m e tryP a ra m s _ fo r_ D e B U G

W _ b 0 =7 .0 uW _ c _ s i c =1 4 5 uW _ c =W _ c _ s i cW _ b =W _ b 0

E qnV ar

H IC U M_ Mo d e lm o n ta

A l lP a ra m s =S e l fh e a ti n g Mo d e l=

A c Mo d e l=Im e l t=Im a x=C th =0 .0 0 0R th =1 0 0T ri s e =T n o m = 2 7 .0 0 A lq a v= 1 .0 0 0 uA l fa v= 5 .4 1 3 uZe ta re = 3 1 4 .9 mZe ta rc x= -2 2 1 .5 mZe ta rb x= 2 .2 8 4 mZe ta rb i= -7 3 .5 0 mA lc e s = 9 .6 6 9 mK t0 = 5 7 .4 9 u

A l t0 = 3 .9 9 4 mA lvs = 6 .0 1 5 mZe ta c i = 0 .0 0 0 A lb = -2 .8 3 3 mV g b = 1 .1 3 4 K rb i =1 .0 0 0A f=2 .0 0 0K f=0 .0 0 0C s u =1 .0 0 0 aR s u =1 .0 0 0 GOh mV p ts =1 .0 0 0 0 0 E +0 2 0Zs =5 0 0 .0 mV d s =1 .9 3 3C js 0 =2 3 .6 8 fFT s f=0 .0 0 0

Ms c =1 .0 0 0Is c s =0 .0 0 0Ms r=1 .0 0 0Ms f=1 .0 0 6Its s =1 .1 4 7 aR c x=5 .6 8 3R e =2 .0 4 7R b x=K _ rb x* 4 .4 7C e o x=5 8 .7 4 fFMb c x=1 .0 9 7Ib c xs =5 0 .1 4 aFb c =0 .0 0 0C c o x=4 9 .3 6 fFV p tc x=1 .0 0 0 0 0 E +0 2 0Zc x=2 7 0 .0 m

V d c x=6 3 7 .7 m VC jc x0 =3 .5 1 0 fFA b e t=4 0 .0 0Ib e ts =0 .0 0 0Mre p =2 .5 5 0Ire p s =3 9 5 .2 fAMb e p =1 .0 6 6Ib e p s =2 .3 2 8 aA l j e p =2 .5 0 0Ze p =3 3 5 .0 mV d e p =9 3 0 .4 m VC je p 0 =2 5 3 .9 fFL a tl= 0 .0 0 0 L a tb = 0 .0 0 0 Fc rb i= 0 .0 0 0

Fq i= 1 .0 0 0 Fg e o = 6 5 5 .7 mFd q r0 =1 .0 0 0 mR b i0 =1 6 .1 7 * K _ rb i0Qa vl = 4 6 3 .5 fFa vl= 1 1 2 .4 mMb c i= 1 .0 2 2 Ib c i s = 1 .0 0 0 0 0 E -0 2 3Mre i= 4 .3 3 1 Ire i s = 3 .5 0 9 pMb e i= 8 9 7 .0 mIb e i s = 9 .9 1 3 3 9 E -0 2 1T r= 5 8 .0 8 pV c e s = 1 1 3 .2 mV p t= 1 .9 5 1

V l im =1 5 6 .5 m VR c i0 =6 .8 0 6 * K _ R C IA lq f=1 .0 0 0 mFth c =0 .0 0 0A lh c =1 5 0 .0 m s e cT h c s =5 .2 2 2 p s e cGtfe =1 7 4 .5 mT e f0 =5 9 9 .1 fs e cT b vl=3 .2 1 5 p s e cD t0 h =4 3 6 .3 fs e cT 0 =K _ ta u f0 * 2 .6 4 3 pV p tc i=1 .0 0 0 0 0 E +0 2 0Zc i=2 7 0 .0 mV d c i =6 3 7 .7 m V * K _ V D C I0C jc i0 =2 8 .1 5 e -1 5 * K _ C J C I0

A l j e i =2 .5 0 0Ze i =3 3 5 .0 mV d e i =9 3 0 .4 m * K _ V D E I0C je i0 =1 5 7 .7 e -1 5 * K _ C J E I0A l i t=4 7 .5 6 mMc f=9 9 2 .0 mH jc i=8 .7 1 5 m * K _ h jc iH je i=4 .9 1 8 * K _ h j e iH fc =1 .0 0 0 * K _ h fcH fe =1 .0 0 0 * K _ h feIc h =1 .0 0 0 0 0 E +0 2 0Qp 0 =K _ q p 0 * 3 4 .6 2 fC 1 0 =K _ c 1 0 * 6 .4 9 5 7 8 E -0 2 9P N P =n oN P N =ye s

H IC U M

H IC U M_ N P NH IC U M1

Mo d e =n o n l i n e a rT ri s e =T e m p =Mo d e l=m o n ta

es

c

th

b

P o rtE m i tte rN u m =3

P o rtS u b s tra teN u m =4

P o rtT H e rm a lN u m =5

P o rtB a s eN u m =2

P o rtC o l l e c to rN u m =1

１：Model paramter list

2：DFM Functions

3： Formulae of carrier’s mobility and bulk resistances

Example of Agilent’s ADS

555

Concepts of the DFM functions

) kT

qVBE(ISkT

qVBEbbNWnDqA

Inc=Ic ibnc exp)exp(__

2_ ⋅≡

−≈

)exp(_

2_

kTqVBE

NLnDqA

IpeIBepe

iepe−=≈

bbNWDeeNWD

eNeWnDqA

bbNWnDqA

IBICBF

ep

bn

iepb

ibnc

____

)__

(

)__

(

_

_2

_

2_

=

⋅

=≡

Ignoring recombination current

•Ni (density of free-electrons)

•N_e, N_b（Donor in the Emitter, Acceptor in the Base

•Dn_b:Diffusion coefficient of electron in the base

•Dp_e, Diffusion coefficient of hole in the emitter

(1) Static Characteristics

=C10/Qb0

666

Concepts of the DFM functions

(2) Early Voltage

Accounts for a equivalent voltage for minority carriers needed to fully-charge QB (base charge) via CJC

(3) Transit time

W_bN_bAQCJCV CBA ⋅⋅==⋅

D_emW_bTF⋅

=2 Accounts for the transit time of

minority carriers traveling in the intrinsic base region with distance of W_B2=m

''''EVBEC

fJCjci

BA

dVdQ

Ch

QV−

=

TF0

777

iee

e

e

e

ee

esbiBi g

nlbWbbp

lb

bWbp

nlbrR ⋅

⋅⋅⋅≡

⎭⎬⎫

⎩⎨⎧

⎟⎠⎞

⎜⎝⎛ −⋅⋅⋅=

__

6.281

121

121

__

00

Base Sheet Rsistance

Current Flowle

be

W_b

Concepts of the DFM functions

(4) Intrinsic base resistance

888

Concepts of the DFM functions

(5) High Injection

( )( )∫

∫⋅

⋅⋅⋅=

⋅⋅=

bw

bw

dxxbNbW

eDmqAeTF

dxxbNqAeIKF

_

02

_

0 __

__

Accounts for the equivalent current providing same amount of currents as that of QB.

2_2

_ sicWsicNqVsi

PT ε⋅

=

2

lim

01

1

⎟⎟⎠

⎞⎜⎜⎝

⎛+

≈

Vvr

vI

ceffCi

ceffCK ( )

( ) cwcN

vV

fANcNqcwr

n

sn

csEcnCi

__

1__

lim

_0

µ

µ

=

⋅=

G-P

HiCUM

999

Formulae of carrier’s mobility and bulk resistances

Mobility of majority carriers ([6][7] [12])

22

1

1

minmaxmin

11αα

µµµµµ

⎟⎠⎞

⎜⎝⎛+

−

⎟⎠⎞

⎜⎝⎛+

−+=

NN

NN ref

l

ref

i

Resistivity

( )( )2_10log110_ ciNcip +⋅=For p-type: C1=-0.699, C2=11.28For n-type: C1=-0.710, C2=11.08

2.01.982.0α2

0.7190.7110.68α1

6.10E+203.41E+203.43E+20Nref2(cm-3)

2.23E+179.20E+169.68E+16Nref1(cm-3)

29.056.143.4µl (cm2V-1s-1)

44.968.552.2µmin (cm2V-1s-1)

470.51414.01417.0µmax (cm2V-1s-1)

BPA-AsParameter

( ) ( )hehe qkTD µ=

Formula for minority carriers

( )TcmGim

i ,,µµ =

101010

Fitting with experimental data

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

1.0E+02

1.0E+16 1.0E+17 1.0E+18 1.0E+19 1.0E+20Impurity Concentration [cm-3]

Res

istiv

ity

Mobility [6,7,12]

10

100

1000

10000

1.0E+14 1.0E+15 1.0E+16 1.0E+17 1.0E+18 1.0E+19

Impurity Concentration [cm-3]D

rift

Mob

ility

[cm

2/V

-s]

Resistivity [11]

N-TYPE

ElectronP-TYPE

Hole

111111

Creation of the DFM function and its implementation

( ) ( ) ( )bNACbNbNVqAC EBTE _,10__10 22 == µ

( )( )

( ) ( )( ) ( )

( )( )

( ) ( )( ) 2

22

2

2

20

2

220

220

0_0___

_

0_0___

0_0___

0_,10_,1010

bNbNbNbN

AEK

bNbNbNbN

AA

bNbNVqAbNbNVqA

bNAcbNAcKC

B

B

B

B

E

E

BTE

BTE

E

E

⋅

⋅⋅=

⋅

⋅=

⋅

⋅=

≡

µµ

µµ

µµ

( ) 10_1010_ CKcCNew ⋅= value extracted

121212

List of DFM functions (1)

--VptK_Vpt

--FthcK_fthc

--ThcsK_thcs

TFTauf0K_tauf0

--Qp0K_Qp0

--HfcK_hfc

--HfeK_hfe

(VA)HjeiK_hjei

(VA)HjciK_hjci

ISC10K_c10

Gummel-PoonHiCUMDFM functionName

( ) ( )( ) 2

22

0_0___

_bNbNbNbN

AeKB

B

⋅

⋅⋅µµ

( )⎟⎟⎠

⎞⎜⎜⎝

⎛− bWbW

Va

T

G _0_exp

KcjcibWbNbWbNAcK 1

0_0____ •

⋅⋅

⋅

( )( )

( )( ) 2

2

2

2

0_0___

0_0___

eNeNeNeN

bNbNbNbN

n

n

n

n

µµ

µµ

( )( )

( )( ) 2

2

2

2

0____

0____

sicNsicNsicNsicN

bNbNbNbN

n

n

n

n

µµ

µµ

0_0____

bWbNbWbNAeK

⋅⋅

⋅

( )( ) 12

12

0_0___

−

−

⋅⋅

bNDebWbNDebW

( )( )

GbWsicW

GbWsicW

sicWsicNn

sicNnsicW

0_2

0_

_2_

0_0_

__

+

+⋅⋅

µµ

bWsicWbWsicW

sicWsicW

_2_0_20_

0__

⋅+⋅+

2

0__

0__

⎟⎟⎠

⎞⎜⎜⎝

⎛sicWsicW

sicNsicN

131313

List of DFM functions (2)

IKF---K_IKF

--TbfvsK_tbfvs

VjxVdxi0K_Vdxi0

CjxCjxi0K_CJxi0

RCRciK_rci

RBMRbxK_rbx

RBRbi0K_rbi0

BF---K_BF

--Tef0K_tef0

--VptK_Vpt

Gummel-PoonHiCUMDFM functionName

2

0__

0__

⎟⎟⎠

⎞⎜⎜⎝

⎛sicWsicW

sicNsicN

( )( )eNheW

eNheWBFK _0_

0___1

2

2

µµ⋅⋅

( )( )

( )( )0_

_0_0_

__0_

_0_0_

__bNDbND

bNbWbNbW

BNDBND

eNeWeNeW

p

p

n

n

⋅⋅

⋅⋅

0_0_

__

__

bWbpbWbp

LeKBEK

⋅

0_0_

__

bwbp

bwbp

0_0___

depcTsicWdepcTsicW

pc_defpc

−−

⋅

KVdxi01

0__K_Ax ⋅⋅bNbN

( )

( )2

2

_0_0_0_ln

____ln

iNbNsicNeN

iNbNsicNeN

⋅

⋅

( )( )sicNc

sicNcsicWbWsicWbW

_0_

0_0___

µµ⋅

⋅⋅

0__

_0_

0___

bNbN

bWbW

eDeDAeK ⋅⋅⋅

141414

Function of BJT physical model card (1)

2E18

3E18

4E18

5E186E187E188E189E18

1E18

1E19

1E-18

1E-16

1E-14

1E-12

1E-10

1E-8

1E-6

1E-4

1E-2

1E0

1E-20

1E2

1E2

1E3

N_b

BF_iIKF_

iIS

_iVA

_i

2E18

3E18

4E18

5E186E187E188E189E18

1E18

1E19

1E-16

1E-15

1E-14

1E-13

1E-12

1E-17

1E-11

0.90

0.95

1.00

1.05

1.10

1.15

0.85

1.20

N_b

VJC_i

VJE_iTF_i

CJE

_iC

JC_i

CJS

_i

2E18

3E18

4E18

5E18

6E18

7E18

8E18

9E18

1E18

1E19

1E1

1E2

1E3

1E4

1

1E5

N_b

RB

_Ver

tical

_bul

kR

BM

_Lat

eral

RC

_iR

E_i

BF

IKF

IS

VA

VJC

VJE

CJE

CJC

TF

RC

RE

RBRBM

SPICE model parameters: Function of (N_b) N_b:doping concentration in the base

151515

Function of BJT physical model card

0.8 0.9 1.0 1.10.7 1.2

5.0E9

1.0E10

1.5E10

2.0E10

2.5E10

3.0E10

0.0

3.5E10

DC.Vbe

fT_v

al

0.8 0.9 1.0 1.10.7 1.2

2

4

6

8

10

12

0

14

DC.Vbe

nf(2

)N

Fmin

0.6 0.7 0.8 0.9 1.0 1.10.5 1.2

1E-8

1E-7

1E-6

1E-5

1E-4

1E-3

1E-2

1E-1

1E-9

2E-1

50

100

150

0

200

DC.Vbe

IB.i

IC.i

IC.i/IB.i

N_B : 2e18 to 1.4e19 cm-3

by 2e18 cm-3

fT-IC

NFmin

NF50

Hfe

ICIB

161616

fT vs. Hfe Scattering Plot

d_fT=18.5

（=62.5-44）

d_Hfe=60

（=150-90）

BJT Physical model card （HiCUM)

d_fT=16

（=49-33）

d_Hfe=70

（=106-36）N_B Gaussian Nominal value=8e18 +/-10%

W_B Gaussian Nominal value=7ucm +/-10%

VBE=0.92V,VC=3VMeasurement data (230 points)

171717

GainCircules modelling result (0.4um*8um*16unit)MeasSim

VBE=0.8V,

Pinset=-5dBm

VBE=0.85V,

Pinset=-5dBm

VBE=0.8V,

Pinset=0dBm

VBE=0.9V,

Pinset=-5dBm

181818

Power Amplifier for PHS applications

1st-Tr.0.4u*16u*4*1

2nd-Tr.04u*16u*8*3

3rd-Tr.0.4u16u*8*12

Pin Pout

Vc1

Vcc3Vcc1,Vcc2

Regulator

Vc2

191919

HiCUM Pin-Pout modelling result (0.4um*16um*4unit)

ConversionGain IC

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

14

16

18

20

12

22

Input Power [dBm]

Conv

ersio

n G

ain

[dB]

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

0.01

0.02

0.03

0.04

0.00

0.05

Input Power [dBm]

Colle

ctor

Cur

rent

[A]

VE=0.80

VE=0.85

VE=0.80

VE=0.90

VE=0.85

VE=0.90

Pin=2.4 GHz

202020

LoadPull modelling result (0.4um*16um*4unit)MeasSim

VBE=0.8V,

Pinset=-5dBm

VBE=0.85V,

Pinset=-5dBm

VBE=0.8V,

Pinset=0dBm

VBE=0.9V,

Pinset=-5dBm

212121

GP modelHicumMeasurement

Split samples（R±10%）Plus 3 different evaluation boards （3states*2）HiCUM model (nominal parameters)

Pin－Gp Pin－Itotal

Comparison with the measurement (1)

T2TK4#1ES ばらつき（R± 10%）サンプル代表6P　vs　シミュレーションPin- Gp

30

31

32

33

34

35

36

37

- 30 - 25 - 20 - 15 - 10 - 5Pin(dBm)

Gp(d

B)

L_1L_2M_1M_2H_1H_2sim- Hicumsim- GP

MC_simulation@Pin=-12dBm

T2TK4#1ES ばらつき（R± 10%）サンプル代表6P　vs　シミュレーションPin- Itotal

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

- 30 - 25 - 20 - 15 - 10 - 5Pin(dBm)

Itota

l(A) L_1

L_2M_1M_2H_1H_2sim- Hicumsim- GP

MC_simulation@Pin=-12dBm

222222

Comparison with the measurement (2)

Measurement 120 samples

Amp_1Tone_NF_MC ＠Pin=-12dBmHicum Physical model cardNB,WB±10%,R±10% 120trials

CW ＠Pin=-12dBmR±10%(3 R conditions） 120 samples

33.0

33.5

34.0

34.5

35.0

0.16 0.17 0.18 0.19 0.20 0.21 0.22Itotal(A)

Gp (d

B)

LMH

Monte-Carlo simulation by the BJT physical model card

△0.6dB

△0.6dB

Good Match between MonteCarlo simulation and measurement

232323

Summary

• Proposed “BJT physical model card” provides– Simple structure

• 9 process variables– N_b,W_b,d_EG,Rpinch, A_e,N_e,W_e N_sic, W_sic

• Formulae by the use of mobility, bulk resistance, Diffusion coefficients.

– Rreasonable prediction of the device and circuits’statistics without going through fabrication process.

242424

References

1. WEB resources http://www.iee.et.tu-dresden.de/iee/eb/hic_new/hic_start.html.2. Michael Schorter and Anjan Chakravorty,”HICUM A Geometry Scalable Physics-Based Compact

Bipolar Transistor model”, Documentation of model level2 version 2.2, August 2005.3. Michael Schorter,”HICUM A Scalable Physics-Based Compact Bipolar Transistor model”,

Description of model version 2.1, December 2000.4. M.Shorter,”RF-Modeling of Bipolar Transistors with HICUM”,Lausanne, Feb.24,2000.5. WEB resources http://eesof.tm.agilent.com/6. D.M.B. Klaassen,,”A Unified Mobility Model for Device Simulation-I. Model Equations and

Concentration Dependence”, Solid-State Electronics Vol.35, No.7, pp.953-959, 1992.7. D.M.B. Klaassen,,”A Unified Mobility Model for Device Simulation-II. Temperature Dependence

of Carrier Mobility and Lifetime”, Solid-State Electronics Vol.35, No.7, pp.961-967, 1992.8. P.A.Hart,”Bipolar and Bipolar-MOS Integration”,Elsevier ISBN 0-444-815104, 1994.9. John D. Cressler and Guofu Niu ,” Silicon-Germanium heterojunction Bipolar Transistors”, Artech

House Publishers, ISBN 1-58053-361-2, 2003.10. John D. Cressler ,”Silicon Heterostructure Handbook”,Tayolr & Francis, ISBN 0-8493-3559-0,

2006.11. S.M.Sze , “Semiconductor Devices, physics and technology 2nd Edition”, John Wiley & Sons, Inc

2001. ISBN 0-471-33372-7. 12. G.D.Masetti, M.Severi and S.Solmi, IEEE Trans. Electron Devices ED-30, 764 (1983).