SPICE Gummel-Poon (SGP) BJT Model - SCU · 2005-04-21 · SPICE Gummel-Poon (SGP) BJT Model S. Saha...

SPICE Gummel-Poon (SGP) BJT Model

HO #8: ELEN 251 - SGP BJT Model S. Saha

• SPICE Gummel-Poon (SGP) model is most widely used in the semiconductor industry.

• SGP model improves dc characterization of EM3 model by a unified approach.

• The SGP unified model was developed to improve:– base-width modulation – high-injection effects– base-widening effect resulting in τF vs. IC.

• The starting point of SGP model is:– EM2-model– two additional diodes in EM2 representing the extra

component of IB for β roll-off at low IC.

SGP BJT Model: Starting Point


E

r'c

r'e

C

C'

E'

Csub

r'bB B'

CjC

CjE

CDC

CDE

ICT = ICC - IEC

IEC/βR

ICC/βF

⎟⎠⎞⎜

⎝⎛ −

′′

1)0(2 eIC kTEEB

nVq

S

⎟⎠⎞⎜

⎝⎛ −

′′

1)0(4 eIC kTCCB

nVq

S

⎟⎠⎞⎜

⎝⎛ −=

⎟⎠⎞⎜

⎝⎛ −=

′′

′′

1

1

eII

eII

kTV CBq

SEC

kTV EBq

SCC

The starting point of SGP model is EM2-model with two extra diodes to account for β roll-off at low current level.

SGP BJT Model: Model Parameters


• EM2-parameter set: dc (EM1) - βF, βR, Tref, Eg (re-define IS in SGP) bulk-ohmic resistors - r'c, r'e, r'b, charge storage effects - CjE0, φE, mE,CjC0, φC, mC, τF,τR Csub

• Extra model parameters: transistor sat. current - ISS (replacement of IS) low-current β roll-off - C2, nE, C4, nC

forward Early voltage - VA

inverse Early voltage - VB

knee current in ln(IC) vs. VBE - IK

inverse knee current - IKR

τF vs. IC model - B

Derivation of ISS


xjE xjCxE xC

BaseEmitter CollectorSpace-chargelayer

Space-chargelayer

)(xε←)(xp

)(xn

x

• Assumptions:– one-dimensional current equations hold– npn-BJT with EB junction forward biased and BC reverse biased– depletion approximation, that is, no mobile charge inside the

depletion region

– BJT gain is high, that is IB ≅ 0.

Derivation of ISS


One-dimensional current equations (HO #2, slide #36) are: Jn = qµnn(x)ε(x) + qDn(dn(x)/dx) (1) Jp = qµpp(x)ε(x) − qDp(dp(x)/dx) (2)

Since, we assume IB ≅ 0,

∴ Jp = hole current in base ≅ 0 and from (2) we get,

or, qµpp(x)ε(x) − qDp(dp(x)/dx) = 0 (3)

here we used, Dn/µn = Dp/µp = kT/q

The direction of the ε-field in (4) aids e- flow from E → C and retards e- flow from C → E.

dxxdp

xpqkT

dxxdp

xpD

p

p )()(

1)()(

1)x( ==∴µ

ε (4)

Derivation of ISS


The e- flow between E and C is given by (1):

Jn = qµnn(x)ε(x) + qDn(dn(x)/dx) (1)

Using (4) in (1) we get:

We integrate (6) over the neutral base width WB from xE to xC .

⎥⎦⎤

⎢⎣⎡ +=∴

dxxdnxp

dxxdpxnxp

DqJ n

n)()()()()(

dxdn

Dqdx

dppnkTJ nnn

)x()x()x()x(

+= µ (5)

[ ])()()( xpxndxd

xpDq

J nn = (6)or,

Derivation of ISS


xjE xjCxE xC

BaseEmitter CollectorSpace-chargelayer

Space-chargelayer

)(xε←)(xp

)(xn

x

[ ]dxxpxndxdqDdxxpJ

C

E

C

E

X

Xn

X

Xn ∫∫ =∴ )()()( (7)

( ) ( )[ ]

∫

−=∴

C

E

X

X

EECCnn

dxxp

xpxnxpxnqDJ

)(

)()((8)

Derivation of ISS


From PN-junction analysis, we know that the pn-product at the edge of the depletion regions are:

Substituting (9) and (10) in (8) we get:

enxnxp

enxnxp

kTV EBq

iEE

kTV CBq

iCC

′′

′′

=

=

2

2

)()(

)()( (9)

(10)

(11)

∫

⎥⎦⎤

⎢⎣⎡ −

=∴

′′′′

C

E

x

x

kTV EBq

kTV CBq

n i

n

dxxp

eenDqJ

)(

2

Derivation of ISS


If A = cross-sectional area of the emitter, then from (11) we can show that:

∫

⎥⎦⎤

⎢⎣⎡ ⎟

⎠⎞⎜

⎝⎛ −−⎟

⎠⎞⎜

⎝⎛ −−

=

′′′′

C

E

x

x

kTV CBq

kTV EBq

n i

n

dxxp

eenADqI

)(

112

(12)

Where In = total dc minority injection current from E → B in the positive x-direction. We have shown in EM1-model:

⎥⎦⎤

⎢⎣⎡ ⎟

⎠⎞⎜

⎝⎛ −−⎟

⎠⎞⎜

⎝⎛ −=

−≡

′′′′

−

11

)modelEM1(

eeI

III

kTV CBq

kTV EBq

S

ECCCCT

(13)

Derivation of ISS


At low level injection, p(x) ≅ NA(x) in the neutral base region where xE ≤ x ≤ xc. Then we can write (12) as:

⎥⎦⎤

⎢⎣⎡ ⎟

⎠⎞⎜

⎝⎛ −−⎟

⎠⎞⎜

⎝⎛ −=

′′′′−

∫11

)(

2

)levellow( eedxxN

nADqI kT

V CBqkT

V EBq

x

xA

n iCT

C

E

(14)

Since xE and xC depend on applied voltages, we define the fundamental constant, ISS @ VBE = 0 = VBC.

Where xE0 and xC0 are the values of xE and xC with applied zero voltages.

(15)∫

≡0

0

)(

2

C

E

x

xA

n iSS

dxxN

nADqI

Derivation of ISS - Base Charge, QB


Again, (14) can be expressed as:

(16)

⎥⎦⎤

⎢⎣⎡ ⎟

⎠⎞⎜

⎝⎛ −−⎟

⎠⎞⎜

⎝⎛ −=

⎥⎦⎤

⎢⎣⎡ ⎟

⎠⎞⎜

⎝⎛ −−⎟

⎠⎞⎜

⎝⎛ −

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

=

′′′′

′′′′

∫

∫

∫

∫

∫

∫

11)(

)(

)(

11)(

)(

)(

0

0

0

0

0

0

0

0

2

2

eedxxp

dxxNqA

dxxNqA

nADq

eedxxNqA

dxxNqA

dxxp

nADqI

kTV CBq

kTV EBq

x

x

x

xA

x

xA

n i

kTV CBq

kTV EBq

x

xA

x

xA

x

x

n iCT

C

E

C

E

C

E

C

E

C

E

C

E

Derivation of ISS - Normalized Base Charge, qb


Defining:

∫

∫

≡

≡′′

′′

0

0

)(

)(

0

)(

)(

C

E

CBC

EBE

x

xAB

Vx

VxB

dxxNqAQ

dxxpqAQ (17)

(18)

⎥⎦⎤

⎢⎣⎡ ⎟

⎠⎞⎜

⎝⎛ −−⎟

⎠⎞⎜

⎝⎛ −=

⎥⎦⎤

⎢⎣⎡ ⎟

⎠⎞⎜

⎝⎛ −−⎟

⎠⎞⎜

⎝⎛ −=

′′′′

′′′′

11

110

eeqI

eeQQII

kTV CBq

kTV EBq

b

SS

kTV CBq

kTV EBq

B

BSSCT

(19)

where qb ≡ QB/QB0 (20)

We get:

Saturation Current ISS - Summary


⎥⎦⎤

⎢⎣⎡ ⎟

⎠⎞⎜

⎝⎛ −−⎟

⎠⎞⎜

⎝⎛ −=

′′′′ 11 eeqII kT

V CBqkT

V EBq

b

SSCT (19)

∫≡

0

0

)(

2

C

E

x

xA

n iSS

dxxN

nADqI

• Eq. (19) is the generalized expression for current source at allinjection levels.

• is a fundamental constant @ VBE = 0 = VBC.

• qb ≡ QB/QB0 is the normalized majority charge in the neutral base region and accurately models base width modulation:– QB0 = majority carrier charge @ VBE = 0 = VBC

– QB = majority carrier charge under applied voltages.

• qb is expressed as bias-dependent measurable parameters in SGP.

Derivation of Base Charge, QB


• In order to evaluate qb, we first determine the components of QB.

• For the simplicity of QB analysis, we assume:– npn-BJT is in saturation, that is, VB'E' > 0 and VB'C' > 0, then

♦ minority carriers are injected into the Base both from Emitter and Collector

♦ from the charge neutrality, total increase in majority carriers in Base = total increase in minority concentration

– superposition of carriers in different regions hold♦ total excess majority carrier density = sum of the excess majority

carrier density due to each junction separately∴ excess majority carrier concentration in base = excess carriers

due to forward voltage [VB'E' + VB'C']

− depletion approximation holds.

Components of Base Charge, QB


If pF(x) = majority carrier concentration in base @ VB'C' = 0 pR(x) = majority carrier concentration in base @ VB'E' = 0 NA(x) = base doping concentration

Then the excess majority carrier concentration in the base is given by: p'(x) = [pF(x) − NA(x)] + [pR(x) − NA(x)] (21)

xjE xjCxE0 xC0Base

Emitt

er

Col

lect

or

↓)(xpF

xxE(VB'E') xC(VB'C')

QEQC

QF

QR

↓)(xp

↓)(xpR

QB0

)(xN A

↑



From (17), the total majority charge in the base is given by:

(22)∫∫

∫′′

′′

′′

′′

′′

′′

′+=

≡

)(

)(

)(

)(

)(

)(

)()(

)(

CBC

EBE

CBC

EBE

CBC

EBE

Vx

Vx

Vx

VxA

Vx

VxB

dxxpqAdxxqAN

dxxqApQ

equilibrium component excess component

The equilibrium component of QB can be split into three-components:

∫∫∫∫′′

′′

′′

′′

++=)(

)(

)(

)( 0

0

0

0

)()()()(CBC

C

C

E

E

EBE

CBC

EBE

Vx

xA

x

xA

x

VxA

Vx

VxA dxxqANdxxqANdxxqANdxxqAN

QE QB0 QC



So that:

∫∫∫∫′′

′′

′′

′′

′+++=)(

)(

)(

)(

)()()()(0

0

0

0 CBC

EBE

CBC

C

C

E

E

EBE

Vx

Vx

Vx

xA

x

xA

x

VxAB dxxpqAdxxqANdxxqANdxxqANQ

QE QB0 QC

(23)∫′′

′′

′+++=∴)(

)(0 )(

CBC

EBE

Vx

VxCBEB dxxpqAQQQQ

xjE xjCxE0 xC0Base

Emitt

er

Col

lect

or

↓)(xpF


QEQC

QF

QR

↓)(xp

↓)(xpR

QB0

)(xN A

↑



From (21) and (23),

(24)RFCBEB QQQQQQ ++++=∴ 0

QF

[ ]

[ ]∫

∫′′

′′

′′

′′

−+

−+++=

)(

)(

)(

)(0

)()(

)()(

CBC

EBE

CBC

EBE

Vx

VxAR

Vx

VxAFCBEB

dxxNxpqA

dxxNxpqAQQQQ

QR

xjE xjCxE0 xC0Base

Emitt

er

Col

lect

or

↓)(xpF


QEQC

QF

QR

↓)(xp

↓)(xpR

QB0

)(xN A

↑



xjE xjCxE0 xC0Base

Emitt

er

Col

lect

or

↓)(xpF


QEQC

QF

QR

↓)(xp

↓)(xpR

QB0

)(xN A

↑

QB0 = charge in the neutral base under VB'E' = 0 = VB'C'. QE = increase in QB under VB'E' and is only a mathematical entity. QC = increase in QB under VB'C' and is only a mathematical entity. QF = excess majority charge in the biased-device with VB'C' = 0. It is

only a mathematical entity and important under high level injection. QR = excess majority charge in the biased-device with VB'E' = 0. It is

only a mathematical entity and important under high level injection.

Components of Normalized Base Charge, qb


From Eq. (24), we get the normalized components of base charge:

rfceb

B

R

B

F

B

C

B

B

B

E

B

B

qqqqqQQ

QQ

QQ

QQ

QQ

QQ

++++=

++++=

10000

0

00

(25)rfceb qqqqq ++++=∴ 1

0

0

0

0

Where,

B

Rr

B

Ff

B

Cc

B

Ee

QQq

QQq

QQq

QQq

≡

≡

≡

≡

Evaluation of qb: Component qe


We defined, QE = increase in the majority charge due to VB'E'.

(26)

∫

∫′′

′′

=

=∴

EB

EB

V

jEB

e

V

jEE

dVVCQ

q

dVVCQ

00

0

)(1and,

)(

(27)

jE

BV

jEEB

BB

B

B

EB

B

EBjEe

jEjEjE

CQ

dVVCV

QV

sVV

VQ

VCq

CCC

EB

0

0

0

0

)(1

:adefinedvoltageEarlyinversewhere

then,

ofvalueaverageconstantAssume,

=≡

=

≡=

=≡=

∫′′

′′

′′′′(28)

(29)

Evaluation of qe


• VB in Eq. (29) models base-width modulation due to the variation of E-B junction depletion layer under VB'E'.

• VB due to VB'E' is the inverse of Early voltage due to VB'C'.

• In Eq (29), VB = constant ⇒ CjE = constant independent of VB'E'.

• Constant CjE is justified as:since QE << QB0

∴ qe << 1 and is not a dominant components of qb.

• VB = constant may cause large error in qe, especially, @ VB'E' > 0.

• The error in (29) due to qe for VB'E' > 0 can be eliminated by:– integrating CjE over the bias range– extracting VB from the slope of ln(IC) vs. qVB'E'/kT plot.

Evaluation of qe


• In order to determine the effect of qe accurately, we set: qc = qr = qf = 0 ⇒ qb = 1 + qe,

• Then from (19) in the normal active region, we have:

• Thus, the slope of IC vs. VB'E' plot is given by:

( ) ⎟⎠⎞⎜

⎝⎛ −

+=

′′ 11 eq

II kTV EBq

e

SSC (30)

( )

( )( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛+

−=⎟⎠⎞

⎜⎝⎛

=

⎟⎟⎠

⎞⎜⎜⎝

⎛+

−=

′′

′′′′

′′

′′

0

0

1)(

1ln1

1)(

1

Be

EBjEC

EBEB

C

C

Be

EBjEC

EB

C

QqVC

qkTI

kTqVd

ddVdI

IqkT

QqVC

qkT

kTqI

dVdI

(31)

Evaluation of qe


• From (31), the slope of ln(IC) vs. qVB'E'/kT plot is given by:

• When CjE = constant ≡ <CjE>, then from (28), qe = VB'E'/VB; and from (29), <CjE> = QB0/VB

therefore, from (32):

(32)

( )

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛+

−=∴

⎟⎟⎠

⎞⎜⎜⎝

⎛+

−=≡

′′

′′

′′=′′

0

0

1)(

1

11

)(111

0

Be

EBjEE

Be

EBjEV

EB

C

CE

QqVC

qkT

n

QqVC

qkT

dVdI

IqkT

n CB

(33)( )⎟⎟

⎠

⎞⎜⎜⎝

⎛+

−≅

′′EBB

E

VVqkT

n11

1

Evaluation of qe: Summary


• For most transistors:– qe = VB'E'/VB

– VB = QB0/<CjE> is the inverse of Early voltage = constant.

• VB = constant ⇒ CjE = constant independent of VB'E'.

• Constant CjE is justified:since QE << QB0

∴ qe << 1 and is not a dominant component of qb

• VB = constant may cause large error in qe, especially, @ VB'E' > 0.

• The error due to qe for VB'E' > 0 can be eliminated by:– integrating CjE over the bias range– extracting VB from the slope of ln(IC) vs. qVB'E'/kT plot.

Evaluation of qb: Component qc


• qc models base-width modulation and therefore, Early voltage by changing depletion layer-width due to VB'C' at low current level.

• Using the procedure used for qe, we can show:

∫′′

=CBV

jCB

c dVVCQ

q00

)(1(34)

jC

BV

jECB

BA

A

A

CB

B

CBjCc

jCjCjC

CQ

dVVCV

QV

VV

VQ

VCq

CCC

CB

0

0

0

0

)(1

bydefinedvoltageEarlywhere

then,

ofvalueaverageconstantAssume,

=≡

=

≡=

=≡=

∫′′

′′

′′′′(35)

(36)

Evaluation of qc


• VA in Eq. (36) models base-width modulation due to the variation of C-B junction depletion layer under VB'C'.

• In Eq (36), VA = constant ⇒ CjC = constant independent of VB'C'.• Constant CjC is justified in the normal active region when B-E

junction is reversed biased, that is, VC'B' < 1. • VA = constant may cause large error in qc, when B-C junction is

forward biased, that is, the device is in:– inverse region– saturation region.

• A more accurate expression for qc is required for accurate modeling of Early voltage in the:– inverse region– saturation region.

Effect of qc on Ic


• The effect of qc on BJT device characteristics in the normal active region is finite output conductance g0.

• In order to determine g0, we set: qe = qr = qf = 0 ⇒ qb = 1 + qc, • Then neglecting bulk-ohmic resistors, we get:

• From (37), we can show:

( )

⎟⎠⎞⎜

⎝⎛ −

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=

⎟⎠⎞⎜

⎝⎛ −

+=

11

11

e

VV

I

eq

II

kTV BEq

A

BC

SS

kTV BEq

c

SSC

(37)

A

C

BECE

C

VI

VdVdIg )0(

constant0 ≅

== (38)

Evaluation of qb: Component qf


• qf can be considered as the normalized excess carrier density in the base with E-B bias VB'E' and models high level injection.

• From charge neutrality: total excess majority carriers = total excess minority carriers.

Therefore, for an npn transistor with |VB'E'| > 0; VB'C' = 0

• QF in (39) (denoted by QB) in EM2 model is given by: QF = QB

EM2 = τBICC (40)

[ ] ∫∫ ⎥⎦

⎤⎢⎣

⎡−=−=

C

E

C

E

x

x A

iF

x

xAFF dx

xNnxnqAdxxNxpqAQ

)()()()(

2

(39)

⎟⎠⎞⎜

⎝⎛ −==∴

′′ 100

eqI

QQIq kT

V EBq

b

SS

B

B

B

CCBf

ττ(41)

Evaluation of qb: Component qr


• qr can be considered as the normalized excess carrier density in the base with C-B bias VB'C' and models high level injection.

• From charge neutrality: total excess majority carriers = total excess minority carriers.

Therefore, for an npn transistor with |VB'C'| > 0; VB'E' = 0

• QR in (42) (denoted by QBR) in EM2 model is given by: QR = QBR

EM2 = τBRIEC (43)

[ ] ∫∫ ⎥⎦

⎤⎢⎣

⎡−=−=

C

E

C

E

x

x A

iR

x

xARR dx

xNnxnqAdxxNxpqAQ

)()()()(

2

(42)

⎟⎠⎞⎜

⎝⎛ −==∴

′′1

00eq

IQQ

Iq kTV CBq

b

SS

B

BR

B

ECBRr

ττ(44)

Solution for qb


• We know:

• Then substituting (28), (35), (41), (44) in (25) we get:

Where τBdc ≡ modified forward base transit time due to mobile charge in

the depletion region (i.e., without depletion approximation).

τBRdc ≡ modified reverse base transit time due to mobile charge in the depletion region (i.e., without depletion approximation).

(25)rfceb qqqqq ++++= 1

⎟⎠⎞⎜

⎝⎛ −+

⎟⎠⎞⎜

⎝⎛ −+++=

′′

′′′′′′

1

11

0

0

eqI

Q

eqI

QVV

VVq

kTV CBq

b

SS

B

BR

kTV EBq

b

SS

B

B

A

CB

B

EBb

dc

dc

τ

τ

(45)q1

q2/qb

Solution for qb


We can simplify (45) to get:

Here

Where q1 in (47) models the base width modulation q2 in (48) models the effect of high level injection.

A

CB

B

EB

VV

VVq ′′′′ ++≡ 11 (47)

(46)b

b qqqq 2

1 +=

02

11

B

kTV CBq

SSBRkTV EBq

SSB

Q

eIeIq

dcdc⎟⎠⎞⎜

⎝⎛ −+⎟

⎠⎞⎜

⎝⎛ −

≡

′′′′ττ

(48)

Solution for qb


• From (45) we get, qb

2 − qbq1 − q2 = 0 (49)

since qb > 0, (50) is obtained taking the positive solution only.

• Equation (50):– offers solution for IC

– defines injection level♦ if q2 << q1

2/4, qb = q1, then qf = qr = 0 ⇒ low level injection♦ if q2 >> q1

2/4 ⇒ high level injection (51) ∴ qb = (q2)1/2 (52)

(50)2

211

22qqqqb +⎟

⎠⎞

⎜⎝⎛+=∴

Solution for qb: High Level Injection


For simplicity, we assume VB'C' = 0 (i.e., qr = 0). Then from (48) and (52), for high level injection in the forward active region:

∴ Substituting for qb in (19), we get for high level injection @ VB'C'= 0 and VB'E' >> kT/q:

(53)kTqV

B

SSB

kTqV

B

SSBb

EBdc

EBdc

eQ

I

eQ

Iqq

2

0

02

′′

′′

=

≅=

τ

τ

kTqV

B

SSB

kTqV

B

SSB

kTV EBq

SS

CTC

EB

dcEB

dc

eIQ

eQ

I

eIII 20

2

0

1 ′′

′′≅

⎟⎠⎞⎜

⎝⎛ −

=≅

′′

ττ(54)

High Level Injection: Knee Current, IK


• For low level injection, if we assume, qe = qc = 0, then qb = 1:

• From (19), we get for low level injection @ VB'C' = 0 and VB'E' >> kT/q:

• The intersection of high current and low current asymptote is given by (IK,VK) where IC(high-level) = IC(low-level).

• Therefore, from (54) and (55):

(55)eII kTV EBq

SSlevellowC′′

− ≅)(

(56)

kTqV

SSK

kTqV

B

SSBK

K

K

dc

eII

eIQI

=

⎟⎟⎠

⎞⎜⎜⎝

⎛= 20

τ

(57)

High Level Injection: Knee Current, IK


• From (56) and (57), we get:

• Similarly, for inverse region:

• Model parameters: (VA, VB, ISS, IK, IKR) are extracted from – ln(IC) vs. VB'E' plot– ln(IE) vs. VB'C' plot.

(58)dcB

BK

QIτ

0= ln(IC)

qVB'E'/kT

VBC = 0

( )KI

slope = 1

slope = 1/2

qVK/kT

ln

(59)dcBR

BKR

QIτ

0=

SGP Model: Summary


(47)

⎟⎠⎞⎜

⎝⎛ −+⎟

⎠⎞⎜

⎝⎛ −=

⎟⎠⎞⎜

⎝⎛ −+⎟

⎠⎞⎜

⎝⎛ −≡

′′′′

′′′′

11

1100

2

eII

eII

eIQ

eIQ

q

kTV CBq

KR

SSkT

V EBq

K

SS

kTV CBq

SSB

BRkT

V EBq

SSB

B dcdcττ

(60)

From (58) and (59)

(50)2

211

22qqqqb +⎟

⎠⎞

⎜⎝⎛+=∴

A

CB

B

EB

VV

VVq ′′′′ ++≡11

where

⎥⎦⎤

⎢⎣⎡ ⎟

⎠⎞⎜

⎝⎛ −−⎟

⎠⎞⎜

⎝⎛ −=

′′′′ 11 eeqII kT

V CBqkT

V EBq

b

SSCT (19)

SGP Model: Summary


• q1 models base-width modulation• q2 models high level injection

– the condition for high level injection:

4

21

2qq ≥

• The model parameters: (VA, VB, ISS, IK, IKR) are extracted from – ln(IC) vs. VB'E' plot in the normal mode of BJT operation– ln(IE) vs. VB'C' plot in the inverse mode of BJT operation– IC vs. VCE characteristics in the normal mode of BJT operation– IE vs. VEC characteristics in the inverse mode of BJT operation.

• A parameter, B is used to model base widening (base push-out) effect at high currents.

Limitations of SGP


Trench-Isolated double-poly NPN• Inability to model collector resistance modulation (quasi-saturation).

• Inability to consider parasitic substrate transistor action.

• Inaccurate Early effect formulation to model output resistance go in narrow-base BJTs.

• Its inability to consider fixed (i.e. bias independent) dielectric capacitances of double poly BJTs for accurate capacitance modeling.

Features of VBIC Model


• Vertical Bipolar Inter-Company (VBIC) model was developed to address the limitations of SGP model.

• Features of VBIC (http://www.designers-guide.com/VBIC/) model: – improved Early effect (go) modeling– quasi-saturation modeling– parasitic substrate transistor modeling– parasitic fixed (oxide) capacitance modeling– avalanche multiplication modeling– improved temperature dependence modeling– de-coupling of base and collector currents– electrothermal (self-heating) modeling– improved heterojunction bipolar transistor (HBT) modeling.

http://www.designers-guide.com/VBIC/

Features of VBIC Model


• VBIC was developed to model:– vertical npn-BJTs– can, also, be used to model vertical pnp-BJTs– can model junction-isolated as well as trench-isolated BJTs.

Junction isolated diffused npn-BJT

VBIC Model - Equivalent Network


Home Work 2: Due April 14, 2005


1) Consider an npn-BJT in the normal active mode of operation.(a) Schematically show the components of base charge responsible for base-width

modulation. Label your plot, show the integration limits to compute charge components, and state your assumptions.

(b) Write down the expression for the normalized base-charge responsible for base-width modulation.

(c) Write down the expression for SGP-model current source for base-width modulation in terms of forward and reverse Early voltages only.

(d) Write down the expression for current source without the base-width modulation. Assume low-level injection.

(e) Show the effect of Eq. in part (c) and (d) on IC vs. VCE plots. Explain.

2) Describe the procedure to extract the following model parameters of an npn-BJT:

(a) transistor saturation current IS, (b) DC current gain βFM, (c) bulk collector ohmic resistor rc', (d) forward knee current IKF.

Home Work 2: Due April 14, 2005


3) For an accurate modeling of BJTs, VBIC-BJT-model was developed to include the parasitic effects. In this problem, you will modify SGP-model for vertical npn-BJTs to include the parasitic vertical pnp-BJT for the advanced BJT structure shown below.

(a) Draw the SGP-equivalent network for the parasitic pnp-BJT.

(b) Use block diagrams to show the effect of parasitic pnp device in the intrinsic npn device model.

(c) Draw the equivalent network of the modified model in part (b) showing all components (ohmic resistors, charge storage elements, etc.).

SPICE Gummel-Poon (SGP) BJT Model - SCU · 2005-04-21 · SPICE Gummel-Poon (SGP) BJT Model S. Saha...

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Transcript of SPICE Gummel-Poon (SGP) BJT Model - SCU · 2005-04-21 · SPICE Gummel-Poon (SGP) BJT Model S. Saha...