vbic fundamentals - designer’s guide2 vbic history review of vbic model improvements over sgp...

VBIC Fundamentals

Colin McAndrew

Motorola, Inc.

2100 East Elliot Rd. MD EL-701

Tempe, AZ 85284 USA

1 VBIC

History

Review of VBIC model improvements over SGP

model formulation

observations and comments

Parameter extraction relationship to SGP

details of specific steps

Practical issues geometry modeling

statistical modeling

Code mechanism for definition and generation

Outline

2 VBIC

A Direct Descendent of BCTM John Shier and Jerry Seitchik were the

prime motivators

many others have provided feedback andsuggestions

Derek Bowers Didier CeliMark Dunn Mark FoisyIan Getreu Terry MageeMarc McSwain Shahriar MoinianKevin Negus James ParkerDavid Roulston Michael SchroterShaun Simpkins Paul van WijnenLarry Wagner

Genesis

3 VBIC

p substrate

p iso

n+ buried layer

n+ sinker

n epi

emitter collectorbasen+p−

Junction Isolated Diffused NPN

4 VBIC

p substrate

n+ buried layer

n+ sinker

n well

polysilicon

trench

polysiliconemitter

isolation

base

base-emitterdielectric overlap

capacitance

base-collectordielectric overlap

capacitance

collector

Trench Isolated Double Poly NPN

5 VBIC

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 514

15

16

17

18

19

20

x

log1

0(N

) (c

m−

3 )

xeb

xbc

xbl

epi

base

emitter

deepcollector

Doping Profile

6 VBIC

improved Early effect modeling

physical separation of and

improved HBT modeling capability

improved depletion, diffusion capacitances

parasitic PNP

modified Kull quasi-saturation modeling

constant overlap capacitances

weak avalanche model

base-emitter breakdown

improved temperature modeling built-in potential does not become negative!

self-heating

incompatibilities between VBIC and SGP Early effect modeling

emitter crowding model

Ic Ib

IRB

VBIC and SGP

7 VBIC

“Good” I c Fit is Not Sufficient, I cro is Important

Vi

Vo

vi vo

go

gmvigπvi

vovi------

gmgo-------

IcVtvg

o---------------≈=

Ic≈ISexp(Vbe/Vtv)

Plot and Fit what is Important for Design

8 VBIC

0 5 10 150

20

40

60

80

100

120

140

160

180

200

Vce

(V)

VA=

I c/go (

V)

data

VBIC

SGP

Early Voltage Modeling

9 VBIC

VBIC 1.2 has reach-through model

−2 −1.5 −1 −0.5 0 0.5 10

0.5

1

1.5

2

2.5

V (V)

C

VBIC

SGP

Depletion Capacitance Modeling

10 VBIC

negative output conductance at high V be

is caused by velocity saturation model

fixed in VBIC

0 0.5 1 1.5 2 2.5 30

2

4

6

8

10

12

14

16

18

20

Vce

(V)

I c (

mA

)

increasingV

be

Problems with Kull

11 VBIC

Effect is visible for 50 µm long devices! convenient to model as mobility reduction

much more informative than velocity-field plot

is 1 for low field, and increase with field E

common models are linear and square-root

linear model is often used for analyticsimplicity (Kull), square-root model issmooth and continuous, and preferredphysically

µred E( ) µo µ E( )⁄=

µred 1µo

vsat----------

VL

------+=

µred 1µo

vsat----------

VL----

2

+=

Ec vsat µo⁄=

Velocity Saturation Modeling

12 VBIC

What does self-heating do to a resistor? resistance change is

temperature rise is

varies nearly as inverse area

resistance varies as

putting this together gives an effectivemobility reduction

the parabolic variation of with field isexactly what is seen in the low field data

accurate velocity saturation modelingmust be done with a self-consistent self-heating model

R R0 1 TC1∆T+( )=

∆T RTHIV RTHV2

R0⁄≈=

RTHRTH RTHA LW( )⁄=

R0 RSL W⁄=

R R0⁄ µred 1RTHATC1

RS--------------------------

V

L----

2+≈=

µred

Velocity Saturation?

13 VBIC

common linear and square root models arenot accurate

0 1 2 3 4 5 60.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

E (V/um)

u red

data

linear model

square root model, varying Ec

asymptotic hard saturation

improved model

Velocity Saturation

14 VBIC

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

Vce (V)

Ic (

mA

)

VBIC Electrothermal HBT Modeling

VBIC

data

Electrothermal Model

15 VBIC

output resistance degradation

10−5

10−4

10−3

10−2

102

103

104

105

106

Ic (A)

Ro (

Ohm

)

electrothermal

isothermal

Need for Electrothermal Modeling

16 VBIC

Itxf -Itzr

c

e

b

RCX

RE

RBX

Ibc-Igc

Ibe

Qbc

Qbe

Itfp -Itrp

Ibcp

Ibep

Qbcp

Qbep

RS

Qbcx

RBIP/qbp

RBI/qb

IbexQbex

CBEO

s CBCO

bx bi

ei

cx

ci

bp

si

RCI

IthCTH

RTH

dt

ItzfQcxf

Flxf

1Ω

xf1 xf2

thermal networktl

excess phase network

VBIC Equivalent Network

17 VBIC

Icc

Itf Itr–

qb----------------=

Itf ISVbei

NFVtv----------------

exp 1–

=

Itr ISVbci

NRVtv----------------

exp 1–

=

qb q1

q2

qb------+=

q1 1qje

VER-----------

qjcVEF----------+ +=

q2

ItfIKF--------

ItrIKR---------+=

Transport Model

18 VBIC

Based on Recombination/Generation

ideal and non-deal components

is of order 1

is of order 2

Ib Ibi Ibn+=

Ibi IBI

VbNIVtv--------------

exp 1–

=

NI

Ibn IBN

VbNNVtv----------------

exp 1–

=

NN

Components of Base Current

19 VBIC

))

continuity equation

carrier densities

drift-diffusion relations

surface recombination

Shockley-Read-Hall process

Auger process

q n∂ t∂⁄( ) Je∇•– q Ge Re–( )=

Vtv kT q⁄=

n nie ψ ϕe–( ) Vtv⁄( )exp=

p nie ϕh ψ–( ) Vtv⁄( )exp=

Je qµen ψ∇– qDe n∇+ qµen ϕe∇–= =

Jh qµhp ψ∇– qDh p∇– qµhp ϕh∇–= =

Jh qSh p p0–( )=

Rsrh np nie2

–( ) τh n nie+( ) τe p nie+(+(⁄=

Raug np nie2

–( ) cen chp+( )=

Basic Modeling Equations

20 VBIC

steady-state, ignore recombination/gen.

for electron quasi-Fermi potential

from the drift-diffusion relation

rearranging and integrating across base

Jex const=

ϕe– Vtv⁄( )exp∂x∂----------------------------------------

ϕe– Vtv⁄( )exp

Vtv-------------------------------------

ϕe∂x∂---------–=

Je qµenieVtv ψ Vtv⁄( )expϕe– Vtv⁄( )exp∂x∂----------------------------------------=

Je

ψ x( )Vtv

------------– exp

µe x( )nie x( )------------------------------- xd0

w

∫

qVtv

ϕewVtv----------–

expϕe0

Vtv---------–

exp–

=

1-Dimensional Base Analysis

21 VBIC

now is constant across the base, so

multiplying by and noting

that junction biases are

saturation current is

normalized based charge is

( is at zero applied bias)

scaled base charge (Gummel number) is

physical basis of BJT behavior is apparent

ϕh

ϕh Vtv⁄( )exp

ϕh ϕe–

Icc

ISVbeiVtv-----------

expVbciVtv-----------

exp–

qb------------------------------------------------------------------------=

IS qAeVtv Gb0⁄=

qb Gb Gb0⁄=

Gb0 Gb

Gb p µenie2( )⁄ xd

0

w

∫=

Gummel ICCR

22 VBIC

in the emitter and , so

and

recombination rates are

in the emitter , so integration

over the emitter gives

this is an ideal component of base current

ϕe 0≈ n Nde≈ p n«

np nie2

»

Rqn srh,pτh-----

nie2 ϕh Vtv⁄( )exp

τhNde

------------------------------------------= =

Rqn aug, cen2p ceNden

ie2 ϕh Vtv⁄( )exp= =

ϕh Vbei≈

Ibe qn, Vbei Vtv⁄( )exp∝

Quasi-Neutral Emitter Base Current

23 VBIC

h))

recombination at the emitter contact

hole density at emitter side of base-emitterjunction is

for a shallow emitter

hole density at the emitter

surface recombination is an idealcomponent of base current

Jh ec, qSh pec pec0–( ) qShpec==

pe b, nie2

Vbei Vtv⁄( )exp Nde⁄=

Jh qDh pe b, pec–( ) we⁄=

pec nie2

Vbei Vtv⁄( )exp Nde 1 Shwe D⁄+((⁄=

Ibe ec, Vbei Vtv⁄( )exp∝

Emitter Contact Base Current

24 VBIC

1+

-----------

in base-emitter space-charge region

but both and are relatively

small: Auger process is negligible

this rate is maximized when

for approximately equal lifetimes

space-charge recombination contributes tonon-ideal component of base current

np nie2

» n p

Rsc srh,nie Vbei Vtv⁄( )exp

τhψ

Vtv--------exp 1+

τe

Vbei ψ–

Vtv---------------------exp

+

----------------------------------------------------------------------------------------=

ψ 0.5 Vbei Vtv τh τe⁄( )log–( )=

Rsc srh, nie τh τe+( )⁄( ) 0.5Vbei Vtv⁄( )exp=

Ibe sc, Vbei 2Vtv( )⁄( )exp∝

Space-Charge Region Base Current

25 VBIC

integrate across the epi region

in the collector , is constant

differentiating w.r.t. position gives

Jex

qµew

---------- n ϕedϕe0

ϕew

∫–=

n p N+= ϕh

np p p N+( ) nie2 ϕh ϕe–

Vtv-------------------

exp= =

x

2p N+( ) p∂x∂------

nie2

Vtv--------–

ϕh ϕe–

Vtv-------------------

ϕe∂

x∂---------exp=

2p N+( )dp npVtv--------– dϕe( )=

n ϕed Vtv 2 Np----+

dp–=

Intrinsic Collector Model

26 VBIC

substitute in integral

implies so

standard quasi-neutrality gives

and similarly for as a function of

Jex

qVtvµe

w------------------ 2 N

p----+

dpp0

pw

∫=

Iepi0

qAVtvµe

w----------------------- 2 pw p0–( ) N

pwp0-------

log+

=

n p N+= pw p0– nw n0–=

pwp0-------

n0

nw-------

Vbcx Vbci–

Vtv-----------------------------

exp=

n0N2---- 1 1

4nie2

N2

-----------VbciVtv-----------

exp++

=

nw Vbcx

Intrinsic Collector Model (cont’d 1)

27 VBIC

1

1----

---------

2------

Final model

empirical modification of velocitysaturation model to prevent negative

and include high bias effects

Iepi0

Vrci Vtv Kbci Kbcx–Kbci +

Kbcx +------------------

log–

+

RCI---------------------------------------------------------------------------------------------=

Kbci 1 GAMM Vbci Vtv⁄( )exp+=

Kbcx 1 GAMM Vbcx Vtv⁄( )exp+=

Irci

Iepi0

1RCIIepi0 VO⁄

1 0.01 Vrci2

+ 2VOHRCF( )⁄+

----------------------------------------------------------------------------------

+

--------------------------------------------------------------------------------------------------=

go

Intrinsic Collector Model (cont’d 2)

28 VBIC

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

Vce (V)

Ic R

cr V

cei V

cbi

Ic

VcbiVcei

Rc-mod

Quasi-saturation Modeling

29 VBIC

in forward operation, ignoring basecurrent, modulation, and parasitics, the

power dissipated is

this is proportional to

Because and are positive,

passivity requires

, i.e.

qb

ISVbe

NFVtv----------------

expVbc

NRVtv----------------

exp–

Vce

1VbeVtv----------

1NR--------

1NF-------–

expVce

NRVtv----------------–

exp–

Vbe Vce

1NR--------

1NF-------– 0≤ NF NR≤

Passivity

30 VBIC

Similar analysis for reverse operationleads to

This implies

The analysis is more restrictive thannecessary, and HBTs most definitely have

, however this shows that with

certain parameter values VBIC (and SGP,and any other BJT model with separateforward and reverse ideality factors) can benon-passive! it is preferred if a model enforces physically

realistic behavior regardless of parameter values

VBIC has and for SGP compatibility and

HBT modeling accuracy

NR NF≤

NR NF≡

NR NF≠

NF NR

Passivity (cont’d)

31 VBIC

significantly increases complexity ofmodel

simpler approaches have proposed (e.g. and correction) but these are not

physically consistent

all branch constitutive relations becomefunctions of local temperature as well asbranch voltages self-consistent with temperature model

is computed as the sum over the non-

storage elements of the product of currentand voltage for every branch cannot simply multiply terminal currents and

voltages because of energy storage elements

Vbe β

Ith

Electrothermal Modeling

32 VBIC

Core Model Similar to SGP program sgp_2_vbic available

simple translations from SGP to VBIC

RBX RBM=

RBI RB RBM–=

CJC CJCXJC=

CJEP CJC 1 XJC–( )=

TD πTFPTF 180⁄=

VBIC Parameters from SGP

33 VBIC

Early Effect Model is Different

specify and for matching

from analysis of output conductance inforward and reverse operation

Vbe Vbe go

gof

Ic------

1 VAF⁄

1 Vbef

VAR⁄ Vbcf

VAF⁄––-----------------------------------------------------------------=

gor

Ie------

1 VAR⁄

1 Vber

VAR⁄ Vbcr

VAF⁄––-----------------------------------------------------------------=

qbcf

cbcf

gof Ic⁄( )

-------------------– qbef

qbcr qber

cber

gor Ie⁄( )

-------------------–

1VEF----------

1VER-----------

1–

1–=

VBIC Parameters from SGP (cont’d)

34 VBIC

specifieddevices

measureddata

“physical”parameters

modelparameters

simulateddata

“physical”parameters

can’t

com

pare

cancompare

What is a Parameter?

35 VBIC

direct extraction is uses simplifications ofa model, it does not give the “best” fit ofthe un-simplified model to data

direct extraction is based on manipulationof a model and data, the quantities fittedare NOT the most important quantities asfar as circuit performance is concerned the goal of characterization is accurate

simulation of important measures ofperformance of circuits, not of unrelatedmetrics of individual devices (at sometimesstrange biases)

models are approximations and trade-offsmust be made during characterization toreflect the modeling needs of targetcircuits for a technology

to optimize the trade-offs you need to fitmultiple targets (g m/Id orIc/go), and these must be weighted overgeometry and bias

Direct Extraction vs. Optimization

36 VBIC

based on a combination of parameterinitialization (extraction) and optimization

both steps use a subset of data and subsetof the model parameters

you can NEVER directly equate a numberderived from simple manipulation ofmeasured data to a a model parameter

proper equivalence involves EXACTLYsimulating and processing data

initial parameters are refined when theapproximate model used as a basis todetermine a parameter is not sufficientlyaccurate

VA VAFSGP

Vbe 1VAF

SGP

VARSGP

---------------+

–=

VBIC Parameter Extraction

37 VBIC

Junction Depletion Capacitance Extraction for each junction measure capacitance

(forward bias is important for )

use optimization to fit model to data

−15 −10 −5 00

20

40

60

80

100

120

140

160

VJ (V)

CJ (

fF)

data

VBIC

Cbe

STEPS: Cbe, Cbc, Ccs

38 VBIC

Coupled Early Voltage Extraction measure forward output (FO) at a moderate

, high enough to get reasonable data

but below where series resistance andhigh-level injection effects are dominant

measure reverse Gummel (RG) data at twovalues of (0 and 1)

differentiate FO data to get

compute and find its maximum value

from RG data compute

where added subscripts mean low andhigh

select one point from the RG data in theregion between where noise and high biaseffects are observable (the “flat” region”)

should be at if possible

Vbe

Veb

go Ic∂ Vce∂⁄=

Ic go⁄

Iel Ieh Iel–( )⁄

Veb

Vbc FCPC<

STEP: VA

39 VBIC

1–

1–

compute junction depletion charges andcapacitances at the selected forward andreverse biases

form and solve the equations

this directly follows from the transportcurrent formulation

you can mix and match derivatives ordifferences for each component, pickingmaximum is useful for FO data as it

avoids data that has a significantavalanche component

qbcfcbcf

gof Ic⁄( )

------------------– qbef

qbcr qberhqberl qberh–( )Iel

Ieh Iel–( )-----------------------------------------–

1VEF----------

1VER----------

=

Ic go⁄

STEP: VA (cont’d)

40 VBIC

Forward Early Effect

0 5 10 150

20

40

60

80

100

120

140

160

180

200

Vce

(V)

VA=

I c/go (

V)

data

VBIC

avalanching not included

STEP: VA (cont’d)

41 VBIC

Reverse Early Effect

0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

Vbc

(V)

VAR

=I c/g

o (V

)

data

VBIC

poorhigh bias effectsdata

STEP: VA (cont’d)

42 VBIC

Substrate Current Analysis

in Forward Gummel (FG) data at

the parasitic base-collector turns on athigh because of de-biasing

under these conditions

at this stage assume that

from the “ideal” region of the

intercept and slope give and

from the deviation from ideality at high

the substrate resistance can be

calculated

really the sum

Vcb 0=

Vbe RC

Is IBCIP

IcRCNCIPVtv----------------------

exp=

NCIP 1=

Is Ic( )IBCIP RC

IcRS

RS RBIP+

STEP: IBCIP

43 VBIC

High Bias FG Data

0.4 0.5 0.6 0.7 0.8 0.9 110

−10

10−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

Vbe

(V)

I (A

)

Ic

Ib Is

data used to get initialestimates of I BCIP, RC, and RS

STEP: IBCIP (cont’d)

44 VBIC

High Bias FG Data, I s(Ic)

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.410

−10

10−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

Ic (mA)

I s (A

)

data

ideal region model

IsRS/RC

slope R C/Vtv

STEP: IBCIP (cont’d)

45 VBIC

FG Data Analysis for I S and NF

select “ideal” region FG data, calculate

, form (accounts for Early effect)

extract and from slope and intercept

0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

35

40

45

Vbe

(V)

d(lo

g(I c))

/d(V

be)

(/V

)

data

model

Icq1 q1Ic

IS NF

STEP: IS

46 VBIC

From FG I b or RG Ib-Is Data

select ideal region data, and follow

from slope and intercept

at low bias, subtract ideal component toget non-ideal component, fit this

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.7510

−13

10−12

10−11

10−10

10−9

10−8

10−7

10−6

Vbe

(V)

I b (A

)

data

model

IBI NI

STEP: IB

47 VBIC

from ideal region RG data extract

from the slope of

from ideal region RG data extract

and from slope and intercept

there is no Early effect in the model for thereverse transport current, so no correction forthis is necessary

Ie NR

q1Ie

Ie ISP

NFP

STEP: ISP

48 VBIC

Same Technique is Used for I KR and IKP select FG high bias data to avoid the

region where the non-ideal component ofbase current is significant

from the ideal component of base currentcalculate the intrinsic base-emitter voltage

calculate from intrinsic biases

approximation: do not know base-collector de-biasing, so assume

from

calculate

calculate

then

Vbei

q1

Vbci Vbc=

Ic IS Vbei NFVtv( )⁄( )exp qb⁄=

qb

q2 qb qb q1–( )=

IKF IS Vbei NFVtv( )⁄( )exp q2⁄=

STEP: IKF

49 VBIC

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 10

5

10

15

20

25

30

35

40

45

50

Vbe

(V)

Bf data

model

fitted at knee

resistive effectsnot yet characterized

STEP: IKF

50 VBIC

Base and Emitter Resistance Characterization the open collector (Giacolleto) method is

used to determine

must be done at very high

initial estimates of and are made

from Ning-Tang analysis

, , , and are

optimized to fit high bias FG data

all of , and are fitted

the residual is , which is symmetric with

respect to relative error, and insensitive tooutliers

proper residual calculation is a key torobust optimization

RE

Ib

RBX RBI

RBX RBI IIKF RC NCIP

Ic Ib Is

y y–y y+------------------

STEP: RB

51 VBIC

Done at high bias physical analysis

derivative is

take derivative, plot versus

abscissa intercept gives , slope gives

optimization is used to refine parameters

Vce IbRE K 1 Ib IOS⁄+( )ln+=

Vce∂Ib∂------------ RE

0.5K

Ib Ib IOS+( )------------------------------------------+ RE

K2Ib--------+≈=

1 Ib⁄

RE K

Open Collector Method for R E

52 VBIC

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 15

10

15

20

25

30

35

40

1/Ib (1/mA)

dVce

/dI b (

Ohm

)

data

linear fit

RE Extraction Plot

53 VBIC

Ning-Tang Analysis

determine from

avoid region where is significant

calculate at three high bias points

Vbei Ib

Ibc

0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 110

−6

10−5

10−4

10−3

10−2

Vbe

(V)

I b (A

)

∆V=Ib(RBX+RBI/qb)+IeRE

∆V/Ib=RE+RBX+RBI/qb+βRE

∆V Ib⁄

Base Resistance DC

54 VBIC

get system of linear equations to solve

however, at high bias ,

therefore the matrix is poorly conditioned

need additional information AC data

physical calculation for (Ning-Tang)

from open collector method

∆VIb

--------

1

∆VIb

--------

2

∆VIb

--------

3

11

qb 1,----------- β1

11

qb 2,----------- β2

11

qb 3,----------- β3

RE RBX+

RBI

RE

=

β βlow qb⁄≈

RBI

RE

Base Resistance DC (cont’d)

55 VBIC

Impedance Circle Method indeterminacy in DC data can be broken

with AC data adds orthogonal information

simple theory gives low frequencyasymptote as and

high frequency asymptote as

because of deviations at high frequency from acircle the high frequency asymptote isextrapolated from low frequency data

however, detailed simulations with arealistic small-signal model show that theradius of the low frequency data dependsstrongly on all components of the small-signal model simple extraction from the impedance circle is

not possible

still should look at this data for extraction

RB rπ 1 βac+( )RE+ +

RB RE+

Base Resistance AC

56 VBIC

∞

Rr ∞

Rk 1

− +

− − + +

− − + +

10−2

10−1

100

101

102

−3

−2

−1

0

1

2

3

ymodel

Res

idua

l

Rk

Rr

∞ydata

n-------------

ydata2

------------- 2ydata nydata

∞ 1– 1n---+

12--- 1 n 1–

1 1– 21 n+( )-----------------+

13---

13--- 1 2

1 n+( )-----------------–

Robust, Symmetric Residuals

57 VBIC

0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 110

−10

10−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

Vbe

(V)

I (A

)

data

VBIC

Ic

Ib

Is

STEP: RB (cont’d)

58 VBIC

Avalanche Parameter Extraction

compute initial and from FO

data at highest

optimize to fit

AVC1 AVC2

Vce

0 5 10 150

20

40

60

80

100

120

140

160

180

200

Vce

(V)

VA=

I c/go (

V)

data

VBIC

VA Ic go⁄=

STEP: AV

59 VBIC

select a target current level in the idealoperating region, calculate at each T

account for temperature dependence

slope of vs. is

from which can be calculated

kept at default value

IS T( ) IS Tnom( )

TTnom--------------

XIS EA–

k q⁄----------1T---

1Tnom--------------–

exp

1NF-------

=

ISq1Ic

Vbe NFVtv( )⁄( )exp--------------------------------------------------=

q1

NF ISlog XIS Tlog– 1 T⁄qEA– k⁄ EA

XIS

Activation Energy Characterization

60 VBIC

Important for Bandgap Design

200 250 300 350 400 4500.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

T (K)

Vbe

@I c=

1.0u

A (

V)

data

VBIC

Vbe vs. Temperature

61 VBIC

initialize and from vs.

optimize to fit data

include shape parameters and

10−8

10−7

10−6

10−5

10−4

10−3

10−2

0

0.5

1

1.5

2

2.5

Ic (A)

f T (

GH

z)

data

VBIC

TF ITF 1 fT⁄ 1 Ic⁄

cbe QTF

fT(Ic) Characterization

62 VBIC

further optimization is used to fit VBIC todata over the complete bias range

temperature coefficients are determined byextracting temperature dependentparameters at different temperatures andthen extracting TC’s from the parameters resistance TC’s from sheet resistance test

structures and measurements

all “standard” extraction data should bewithout self-heating low bias or pulsed measurements

over temperature

thermal resistance is extracted byoptimization to fit high data

the transit time model is identical to that ofSGP and so existing techniques can bedirectly used for or s-parameter

modeling

IcVce

fT Ic( )

Miscellaneous

63 VBIC

0.4 0.5 0.6 0.7 0.8 0.9 110

−10

10−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

Vbe

(V)

I (A

)

data

VBIC

FG Current Modeling

64 VBIC

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 10

5

10

15

20

25

30

35

40

45

50

Vbe

(V)

Bf data

VBIC

FG Beta Modeling

65 VBIC

initialize collector resistance parameters

“smart” way to initialize and ?

optimize to fit saturation characteristics

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

1

2

3

4

5

6

data

VBIC

Vce

(V)

I c (m

A)

GAMM VO

DC Quasi-saturation

66 VBIC

quasi-saturation region behavior cannot bemodeled well with SGP

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

1

2

3

4

5

6

Vce

(V)

I c (m

A)

hi RC SGP

lo RC SGP

DC Quasi-saturation

67 VBIC

all capacitances and currents should bemodeled using area and perimetercomponents (and corner components ifnecessary), e.g.

unless there is a very substantialdifference between a masked dimensionand an effective electrical dimension, thearea and perimeter can be computed as

it is not possible to distinguish between a “delta”between masked and effective dimensions andvariations in the perimeter component

forward transit time is also modeled witharea and perimeter components

so

IS AeISA PeISP+=

Ae WeLe= Pe, 2 We Le+( )=

Qdiff AeISATFA

PeISPTFP

+∝ ISTF

=

TF

AeISATFA

PeISPTFP

+

AeISA PeISP+------------------------------------------------------------=

Geometry Modeling

68 VBIC

similarly from the SGP model the area andperimeter components of collector currentare

want

equating these gives

AeISA

VbeVtv----------

exp 1Vbc

VAFA--------------–

PeISP

VbeVtv----------

exp 1Vbc

VAFP--------------–

Ic I=S

VbeVtv----------

exp 1VbcVAF----------–

1VAF----------

AeISAVAFA----------------

PeISPVAFP----------------+

AeISA PeISP+---------------------------------------=

Geometry Modeling (cont’d)

69 VBIC

Expect the Unexpected! non-ideal component of base current does

not always scale with perimeter

have seen collector resistance increase asemitter length increases

Le

IBEN

expected

observed

Always Verify Geometry Models

70 VBIC

This is the most difficult think in terms of conductance, not

resistance

for small emitters the n=4 model isreasonable for highly doped base rings

as emitter length increases the effectivenumber of base contacts changes

use

rather than for

monotonic decrease in with

number ofbase contacts

1st ordertheory

physicalsimulation

reality

n=1 1/3 ?

n=2 1/12 1/12 ?

n=4 1/32 1/28.6 ?

RBI knρsbe We Le⁄( )=

1 1 k1⁄ 1 k4⁄ 1 k1⁄–( ) We Le⁄( )+( )⁄k1 k1 k4–( ) We Le⁄( )–

RBI Le

Resistance Geometry Modeling

71 VBIC

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

20

40

60

80

100

120

140

160

180

200

W/L

R

1/12-(1/12-1/28.6)W/L

1/(12+(28.6-12)W/L)

RBI increases as emitter length increases!

increasinglength

RBI Variation with Geometry

72 VBIC

Effective Base Structure Varies with Geometry

effectively4 base contacts

effectively single base contact

Base Structure

73 VBIC

Expect a 1/L Dependence for R BX

????

asymptotically correct as gets large

RBX R0 RL L⁄+=

Iδ Gδ Lδ∝ ∝

GBX 1 RBX⁄ G0 GLL+= =

L

Conductance Increases with Width

74 VBIC

must be based on process and geometrydependent models

process dependence defined by Ida andDavis, BCTM89

most efficient and accurate way isbackward propagation of variance (BPV) provides Monte Carlo (distributional) and case

models

for inter-die variation

defined in BCTM97 and SISPAD98

exactly the same modeling basis and BPVcharacterization methodology can beapplied to intra-die variation (mismatch),see Drennan BCTM98

Statistical Modeling

75 VBIC

Complete VBIC Code is Available the only rational way to define a compact

model is in terms of a high-level symbolicdescription not through 40 SPICE subroutines

historically there have been severalproprietary languages and modelinterfaces MAST for Saber (Analogy)

ADMIT for Advice (Lucent)

ASTAP/ASX (IBM)

TekSpice (Tektronix/Maxim)

MDS (Hewlett-Packard)

probably others

VBIC had its own symbolic definition

VHDL-A looked promising, but appears tohave been overtaken by Verilog-A in theindustry

VBIC Code

76 VBIC

VBIC is Defined in Verilog-A well, really in a subset of Verilog-A

conditional definition of 8 separate versions, 3-and 4-terminal, iso-thermal and electro-thermal,and constant- and excess-phase

automated tools generate implementablecode FORTRAN and C

probably Perl

looking at XSPICE

DC and AC solvers are provided

transient and other types of analysesdepend on simulator algorithms can use Verilog-A description

this can be very slow

http://www-sm.rz.fht-esslingen.de/institute/iafgp/neu/VBIC/index.html

VBIC Code (cont’d)

77 VBIC

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0 0.5 1.0 1.5 2.0 2.5 3.0

Im(S

11)

F (GHz)

Vbe=0.766 data Vbe=0.766 VBIC Vbe=0.927 data Vbe=0.927 VBIC Vbe=1.082 data Vbe=1.082 VBIC

-0.2

0

0.2

0.4

0.6

0.8

0 0.5 1.0 1.5 2.0 2.5 3.0

Re(

S11

)

F (GHz)


VBIC s11 Modeling

78 VBIC

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 0.5 1.0 1.5 2.0 2.5 3.0

Im(S

12)

F (GHz)


0

0.05

0.1

0.15

0.2

0 0.5 1.0 1.5 2.0 2.5 3.0

Re(

S12

)

F (GHz)


VBIC s12 Modeling

79 VBIC

0

1

2

3

4

5

6

7

8

0 0.5 1.0 1.5 2.0 2.5 3.0

Im(S

21)

F (GHz)


-14

-12

-10

-8

-6

-4

-2

0

0 0.5 1.0 1.5 2.0 2.5 3.0

Re(

S21

)

F (GHz)


VBIC s21 Modeling

80 VBIC

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.5 1.0 1.5 2.0 2.5 3.0

Re(

S22

)

F (GHz)


-0.3

-0.25

-0.2

-0.15

0 0.5 1.0 1.5 2.0 2.5 3.0

Im(S

22)

F (GHz)


VBIC s22 Modeling

81 VBIC

s-parameter fits have been done to SGPand VBIC to the same data

in the same optimization tool

comparison of RMS errors over bias andfrequency

s-parameterSGP RMS

% errorVBIC RMS

% error

Re(s11) 99.9 7.0

Im(s11) 65.2 6.2

Re(s12) 112.6 12.0

Im(s12) 34.6 6.9

Re(s21) 209.6 14.3

Im(s21) 81.6 8.3

Re(s22) 31.3 8.5

Im(s22) 63.8 8.5

VBIC s-Parameter Modeling

82 VBIC

vbic fundamentals - designer’s guide2 vbic history review of vbic model improvements over sgp...

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