L15 05Mar02 1

Semiconductor Device Modeling and CharacterizationEE5342, Lecture 15 -Sp 2002

Professor Ronald L. Carterronc@uta.edu

http://www.uta.edu/ronc/

L15 05Mar02 2

Charge componentsin the BJT

From Getreau, Modeling the Bipolar Transistor,Tektronix, Inc.

L15 05Mar02 3

Gummel-Poon Staticnpn Circuit Model

C

E

B

B’

ILC

ILEIBF

IBR

ICC - IEC =

IS(exp(vBE/NFVt

- exp(vBC/NRVt)/QB

RC

RE

RBB

L15 05Mar02 4

Gummel-Poon Staticnpn Circuit Model

C

E

B

B’

ILC

ILEIBF

IBR

ICC - IEC =

IS(exp(vBE/NFVt

- exp(vBC/NRVt)/QB

RC

RE

RBB

L15 05Mar02 5

Gummel-Poon Static Par.NAME PARAMETER UNIT DEFAULTIS transport saturation current A 1.0e-16BF ideal maximum forward beta - 100NF forward current emission coef. -1.0VAF forward Early voltage V infiniteISE B-E leakage saturation current A 0NE B-E leakage emission coefficient -1.5BR ideal maximum reverse beta - 1NR reverse current emission coefficient - 1VAR reverse Early voltage V infiniteISC B-C leakage saturation current A 0NC B-C leakage emission coefficient - 2EG energy gap (IS dep on T) eV 1.11XTI temperature exponent for IS - 3

L15 05Mar02 6

Gummel-Poon StaticModel ParametersNAME PARAMETER UNIT DEFAULTIKF corner for forward beta A infinite

high current roll-offIKR corner for reverse beta A infinite

high current roll-offRB zero bias base resistance W 0IRB current where base resistanceA infinite

falls halfway to its min valueRBM minimum base resistance W RB

at high currentsRE emitter resistance W 0RC collector resistance W 0TNOM parameter - meas. temperature °C

27

L15 05Mar02 7

Gummel Poon npnModel Equations

IBF = ISexpf(vBE/NFVt)/BF

ILE = ISEexpf(vBE/NEVt)

IBR = ISexpf(vBC/NRVt)/BR

ILC = ISCexpf(vBC/NCVt)

QB = (1 + vBC/VAF + vBE/VAR )

{ + + (BFIBF/IKF + BRIBR/IKR)}

L15 05Mar02 8

Gummel PoonBase ResistanceIf IRB = 0, RBB = RBM+(RB-RBM)/QB

If IRB > 0RB = RBM + 3(RB-RBM)(tan(z)-z)/(ztan2(z))

[+iB/(IRB)]1/2-

(/)(iB/IRB)1/2z =

Regarding (i) RBB and (x) RTh on slide 22,

RB = RBM + R/(1+iB/IRB)RB , R = RB - RBM

L15 05Mar02 9

BJT CharacterizationForward GummelvBCx= 0 = vBC + iBRB - iCRC

vBEx = vBE +iBRB +(iB+iC)RE

iB = IBF + ILE =

ISexpf(vBE/NFVt)/BF

+ ISEexpf(vBE/NEVt)

iC = FIBF/QB =

ISexpf(vBE/NFVt)/QB

+

-

iC RC

iB

RE

RB

vBEx

vBC

vBE

+

+

-

-

L15 05Mar02 10

Ideal F-G DataiC and iB (A)

vs. vBE (V)

N = 1 1/slope = 59.5 mV/dec

N = 2 1/slope = 119 mV/dec

BJ T I (A) vs. Vbe (V) for the G-P model Forward Gummel configuration (Vbcx=0)

1.E-16

1.E-15

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

0.0 0.2 0.4 0.6 0.8

I c

I b

L15 05Mar02 11

BJT CharacterizationReverse Gummel

+

-

iE

RC

iB

RE

RB

vBCx

vBC

vBE

+

+

-

-

vBEx= 0 = vBE + iBRB - iERE

vBCx = vBC +iBRB +(iB+iE)RC

iB = IBR + ILC =

ISexpf(vBC/NRVt)/BR

+ ISCexpf(vBC/NCVt)

iE = RIBR/QB =

ISexpf(vBC/NRVt)/QB

L15 05Mar02 12

Ideal R-G DataiE and iB (A)

vs. vBE (V)

N = 1 1/slope = 59.5 mV/dec

N = 2 1/slope = 119 mV/dec

BJ T I (A) vs. Vbe (V) for the G-P model Forward Gummel configuration (Vbcx=0)

1.E-16

1.E-15

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

0.0 0.2 0.4 0.6 0.8

I c

I b

Ie

L15 05Mar02 13

emitter

base

collector

reg 4reg 3reg 2reg 1

coll. base & emitter contact regions

Distributed resis-tance in a planar BJT

• The base current must flow lateral to the wafer surface

• Assume E & C cur-rents perpendicular

• Each region of the base adds a term of lateral res.

vBE diminishes as current flows

L15 05Mar02 14

Simulation of 2-dim. current flow

• Distributed device is repr. by Q1, Q2, … Qn

• Area of Q is same as the total area of the distributed device.

• Both devices have the same vCE = VCC

• Both sources have same current iB1 = iB.

• The effective value of the 2-dim. base resistance isRbb’(iB) = V/iB = RBBTh

VCC

QnRR

Q2iBiB1

Q Q1R

=

V

L15 05Mar02 15

Analytical solutionfor distributed Rbb

• Analytical solution and SPICE simulation both fit

RBB = Rbmin + Rbmax/(1 + iB/IRB)RB

xi

Lr

dx

xdv

NEV

vLJ

NFV

vLJ

dxxdi

BBiBE

t

BESE

t

BES

B

expexp

L15 05Mar02 16

Distributed baseresistance function

Normalized base resis-tance vs. current. (i) RBB/RBmax, (ii) RBBSPICE/RBmax, after fitting RBB and RBBSPICE to RBBTh (x) RBBTh/RBmax.

FromAn Accurate Mathematical Model for the Intrinsic Base Resistance of Bipolar Transistors, by Ciubotaru and Carter, Sol.-St.Electr. 41, pp. 655-658, 1997.

RBBTh = RBM +

R/(1+iB/IRB)RB

(R = RB - RBM )

L15 05Mar02 17

Gummel PoonBase ResistanceIf IRB = 0, RBB = RBM+(RB-RBM)/QB

If IRB > 0RB = RBM + 3(RB-RBM)(tan(z)-z)/(ztan2(z))

[+iB/(IRB)]1/2-

(/)(iB/IRB)1/2z =

Regarding (i) RBB and (x) RTh on previous slide,

RBB = Rbmin + Rbmax/(1 + iB/IRB)RB

L15 05Mar02 18

Gummel-Poon Staticnpn Circuit Model

C

E

B

B’

ILC

ILEIBF

IBR

ICC - IEC =

IS(exp(vBE/NFVt

- exp(vBC/NRVt)/QB

RC

RE

RBB

L15 05Mar02 19

Gummel Poon npnModel Equations

IBF = IS expf(vBE/NFVt)/BF

ILE = ISE expf(vBE/NEVt)

IBR = IS expf(vBC/NRVt)/BR

ILC = ISC expf(vBC/NCVt)

ICC - IEC = IS(exp(vBE/NFVt - exp(vBC/NRVt)/QB

QB = { + + (BF IBF/IKF + BR IBR/IKR)1/2} (1 - vBC/VAF - vBE/VAR )-1

L15 05Mar02 20

iE = - IEC =

(IS/QB)exp(vBC/NRVt),

where ICC = 0, and

QB-1

=

(1-vBC/VAF-vBE/VAR )

{IKR terms}-1,

so since vBE = vBC - vEC,

VAR = iE/[iE/vBE]vBC

VAR ParameterExtraction (rEarly)

+

-+

-

iE

iB

vECvBC

0.2 < vEC < 5.0

0.7 < vBC < 0.9

Reverse Active Operation

L15 05Mar02 21

0.0000

0.0002

0.0004

0.0006

0 1 2 3 4 5

iE(A) vs. vEC (V)

Reverse EarlyData for VAR• At a particular data

point, an effective VAR value can be calculated

VAReff = iE/[iE/vBE]vBC

• The most accurate is at vBE = 0 (why?)

vBC = 0.85 V

vBC = 0.75 V

L15 05Mar02 22

+

-+

-

VAF ParameterExtraction (fEarly)

iC

iB

vCEvBE

0.2 < vCE < 5.0

0.7 < vBE < 0.9

Forward Active Operation

iC = ICC =

(IS/QB)exp(vBE/NFVt),

where ICE = 0, and

QB-1

=

(1-vBC/VAF-vBE/VAR )

{IKF terms}-1,

so since vBC = vBE - vCE,

VAF = iC/[iC/vBC]vBE

L15 05Mar02 23

0.000

0.001

0.002

0.003

0 1 2 3 4 5iC(A) vs. vCE (V)

Forward EarlyData for VAF• At a particular data

point, an effective VAF value can be calculated

VAFeff = iC/[iC/vBC]vBE

• The most accurate is at vBC = 0 (why?)

vBE = 0.85 V

vBE = 0.75 V

L15 05Mar02 24

BJT CharacterizationForward GummelvBCx= 0 = vBC + iBRB - iCRC

vBEx = vBE +iBRB +(iB+iC)RE

iB = IBF + ILE =

ISexp(vBE/NFVt)/BF

+ ISEexpf(vBE/NEVt)

iC = FIBF/QB =

ISexp(vBE/NFVt)

(1-vBC/VAF-vBE/VAR )

{IKF terms}-1

+

-

iC RC

iB

RE

RB

vBEx

vBC

vBE

+

+

-

-

L15 05Mar02 25

Region a - IKFIS, RB, RE, NF, VAR

Region b - IS, NF, VAR, RB, RE

Region c - IS/BF, NF, RB, RE

Region d - IS/BF, NFRegion e - ISE, NE

Forward GummelData Sensitivities

1.E-12

1.E-10

1.E-08

1.E-06

1.E-04

1.E-02

0.1 0.3 0.5 0.7 0.9

iC(A),iB(A) vs. vBE(V)

iC

vBCx = 0

iB

a

b

c

d

e

L15 05Mar02 26

Region (a) fgData SensitivitiesRegion a - IKFIS, RB, RE, NF, VARiC = FIBF/QB = ISexp(vBE/NFVt)

(1-vBC/VAF-vBE/VAR ){IKF terms}-1

L15 05Mar02 27

Region (b) fgData SensitivitiesRegion b - IS, NF, VAR, RB, REiC = FIBF/QB = ISexp(vBE/NFVt)

(1-vBC/VAF-vBE/VAR ){IKF terms}-1

L15 05Mar02 28

Region (c) fgData SensitivitiesRegion c - IS/BF, NF, RB, REiB = IBF + ILE = (IS/BF)expf(vBE/NFVt)

+ ISEexpf(vBE/NEVt)

L15 05Mar02 29

Region (d) fgData SensitivitiesRegion d - IS/BF, NFiB = IBF + ILE = (IS/BF)expf(vBE/NFVt)

+ ISEexpf(vBE/NEVt)

L15 05Mar02 30

Region (e) fgData SensitivitiesRegion e - ISE, NE iB = IBF + ILE = (IS/BF)expf(vBE/NFVt)

+ ISEexpf(vBE/NEVt)