L14 March 3 1

EE5342 – Semiconductor Device Modeling and CharacterizationLecture 14 - Spring 2005

Professor Ronald L. Carterronc@uta.edu

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

L14 March 3 2

Re{Y} vs. frequency

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10

Y-parameter data

300 mV

700 mV

1000 mV

800 mV

900 mV

500 mV

L14 March 3 3

Im{Y} vs. frequency

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10

Y-parameter data

300 mV

700 mV

1000 mV

800 mV900 mV

500 mV

L14 March 3 4

Bipolar junctiontransistor (BJT)• The BJT is a “Si

sandwich” Pn (P=p+,=p-) or Np(N=n+, =n-)

• BJT action: npn Forward Active when VBE > 0 and VBC < 0

P n

E B C

VEB VCB

Charge neutral Region

Depletion Region

L14 March 3 5

BJT coordinatesystems

0

z

x”cx”

0 WB WB+WC-WE

0 xB x0x’Ex’

Charge neutral RegionDepletion Region

Base CollectorEmitter

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BJT boundary andinjection cond (npn)

0p

p , V

Vfexppp

0p

p , V

Vfexppp

C

C

2i

E

E

2i

x"xnC

Nn

0nCt

BC0nC0"xnC

x'xnE

Nn

0nEt

BE0nE0'xnE

L14 March 3 7

BJT boundary andinjection cond (npn)

.

V

Vfexpnn

n , V

Vfexpnn

dependent

-inter are BC Base the that Note

t

BC0pBxBxpB

Nn

0pBt

BE0pB0xpB

B

2i

L14 March 3 8

IC npn BJT(*Fig 9.2a)

L14 March 3 9

npn BJT bandsin FA region

qVBC

qVBE

q(VbiE-VBE ) q(VbiC-VBC )

injection high field

L14 March 3 10

Coordinate system - prototype npn BJT (Fig 9.8*)

L14 March 3 11

Notation fornpn & pnp BJTs• NE, NB, NC E, B, and C doping (maj)

• xE, xB, xCE, B, and C CNR widths

• DE, DB, DC Dminority for E, B, and C

• LE, LB, LCLminority for E, B, and C(L2

min = Dmin min)

E0, B0, C0 minority carrier life- times for E, B, and C regions

L14 March 3 12

Notation fornpn BJTs only• pEO, nBO, pCO: E, B, and C thermal

equilibrium minority carrier conc

• pE(x’), nB(x), pC(x’’): positional mathe- matical function for the E, B, and C total minority carrier concentrations

pE(x’), nB(x), pC(x’’): positional ma- thematical function for the excess minority carriers in the E, B, and C

L14 March 3 13

Notation forpnp BJTs only• nEO, pBO, nCO: E, B, and C thermal

equilibrium minority carrier conc

• nE(x’), pB(x), nC (x’’): positional mathe- matical function for the E, B, and C total minority carrier concentrations

nE(x’), pB(x), nC(x’’): positional ma- thematical function for the excess minority carriers in the E, B, and C

L14 March 3 14

npn BJT boundary conditions

0xp ,1VV

expp0x"p :C

etc. ,Nn

n ,1VV

expnxn

,1V

Vexpn0xn :B

1V

Vexpp0p ,0xx'p :E

CCt

BC0CC

B

2i

0Bt

BC0BBB

t

BE0BB

t

BE0EEEE

L14 March 3 15

Emitter solutionin npn BJT

EEE

E

t

BE

E

E

E

E

t

BE

E

Lxx

xx

V

V

L

xL

xx

V

V

x

, '

1exppx'p

sinh

'sinh1expp

x'p

ppp , 0x'p

x'

'pD

E0E

E0

E

E0EE0

E2

E2

E

L14 March 3 16

Base solutionin npn BJT

Bt

BC

Bt

BEB0

BBBt

BC

B

B

t

BE

B

B

B0B

B0BB0BB

B2B

2

xx

VV

fxx

1V

Vfn

Lx when and Lx

VV

f

Lxx

V

Vf

Lx

nxn

nnn , 0D

xn

x

xn

expexp

sinhexp

sinhexpsinh

L14 March 3 17

Collector solutionin npn BJT

CCtBCC

C0C

C

C

C

C

t

BCC0

C

C0CC0CC

C2

C2

Lx , VV , L

"xpx"p

Lx

sinh

L"xx

sinh1VV

expp

x"p

ppp , 0D

x"p

x"

"xp

L14 March 3 18

Hyperbolic sinefunction

Lx

Lx

sinh0Lx

giving,

Lx

1Lx

1

Lx

1Lx

1

Lx

sinh L, x if so

...!2

yy1e ,

ee

eeLx

sinh

itlim

2y

L/xL/x

L/xL/x

L14 March 3 19

npn BJT regionsof operation

VBE

VBC

Forward Active

Reverse Active

Saturation

Cutoff

L14 March 3 20

npn FA BJT minoritycarrier distribution (Fig 9.4*)

L14 March 3 21

npn RA BJT minoritycarrier distribution (Fig 9.11a*)

L14 March 3 22

npn cutoff BJT mincarrier distribution (Fig 9.10a*)

L14 March 3 23

npn sat BJT minoritycarrier distribution (Fig 9.10b*)

L14 March 3 24

Defining currents inFA mode npn BJT (Fig 9.13*)

L14 March 3 25

References

1 OrCAD PSpice A/D Manual, Version 9.1, November, 1999, OrCAD, Inc.

2 Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, 1993.

* Semiconductor Physics & Devices, by Donald A. Neamen, Irwin, Chicago, 1997.