May 4, 2007 1. Current-voltage characteristics of ideal ... · B E B B E B depletion charge in base-emitter SCR depletion charge in base-collector SCR C minority carrier charge in

6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 36-1

Lecture 36 - Bipolar Junction Transistor

(cont.)

May 4, 2007

Contents:

1. Current-voltage characteristics of ideal BJT (cont.)

2. Charge-voltage characteristics of ideal BJT

3. Small-signal behavior of ideal BJT

Reading material:

del Alamo, Ch. 11, §§11.2 (11.2.5), 11.3, 11.4 (11.4.1)

Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


Key questions

• How do the output characteristics of the ideal BJT look like?

• How do the charge-voltage characteristics of the ideal BJT look

like?

• What is the topology of the small-signal equivalent circuit model

of the ideal BJT in FAR?

• What are the key dependencies of its elements?



1. Current-voltage characteristics of ideal BJT (cont.)

Ideal BJT current equations (superposition of forward active + re

verse):

IC = IS(expqVBE

kT − exp

qVBC

kT ) −

IS

βR

(expqVBC

kT − 1)

IB = IS

βF

(expqVBE

kT − 1) +

IS

βR

(expqVBC

kT − 1)

IE = − IS

βF

(expqVBE

kT − 1) − IS(exp

qVBE

kT − exp

qVBC

kT )

Equivalent circuit model representation:

C

IS (exp qVBC -1)

βR kT

qVBE qVBCB IS (exp - exp )kT kT

IS (exp qVBE -1)

βF kT

E

Complete model has only three parameters: IS, βF , and βR.


- -

- -


� Common-emitter output I-V characteristics

vs. VCB:

IC

C

0

forward active

sa

tura

tio

n

cut-off

- +VBC

IB+ B VCE+

VBE IB=0

E 0

VCB

VBC,on

vs. VCE:

IC

C

sa

tura

tio

n

IB=0

E reverse 0

cut-off VCE=VCB+VBE0

forward active- + VBC

IB+ B VCE+

VBE

VCE,sat

VCEsat = −VBCon + VBEon



IC vs. VCB with IB as parameter:



Where is the reverse regime?



Common-emitter output characteristics:



Zoom into inverse regime:



2. Charge-voltage characteristics of ideal BJT

In BJT, two types of stored charge:

• depletion layer charge

• minority carrier charge

In forward-active regime:

B E B B E B

depletion charge�

in base-emitter SCR depletion charge�

in base-collector �

SCR

C

minority carrier �

charge in�

emitter QNR minority carrier �

charge in�

base QNR�

�

C


�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�


� Depletion layer charge

In B-E and B-C SCR’s, respectively:

�

2�qNENB(φbiE − VBE)QjE = AE

NE + NB

� 2�qNBNC(φbiC − VBC)QjC = AC

NB + NC

φbiE and φbiC are respective built-in potentials.

Since NE � NB � NC,

QjE � AE 2�qNB(φbiE − VBE)

QjC � AC 2�qNC(φbiC − VBC)

Depletion capacitance:

∂QjE � �qNB Cjeo

Cje = � AE�= �

∂VBE 2(φbiE − VBE) 1 − VBE

φbiE

∂QjC � �qNC Cjco

Cjc = � AC�

= �

∂VBC 2(φbiC − VBC) 1 − VBC

φbiC



� Minority carrier charge

Excess minority carriers in QNR’s ⇒ excess majority carriers to keep

quasi-neutrality ⇒ diffusion capacitance.

Key result from pn diode: in ”short” or ”transparent” QNR:

stored charge = minority carrier transit time

× injected minority carrier current

• For emitter in FAR:

pE

pE(VBE)

IB

ni2

NE

-xBE x-WE-xBE

QE

QE = τtEIB

with hole transit time:

W 2

τtE = E

2DE



• For base in FAR:

nB

nB(VBE)

IC

nB(WB)=0ni2

NB

0 xWB

QB

QB = τtBIC

with electron transit time:

W 2

τtB = B

2DB



Comments:

• Units of QE and QB are C.

• QE and QB scale with AE.

Total minority carrier charge in FAR:

τtE QF = QE + QB = τtEIB + τtBIC = ( + τtB)IC = τFIC

βF

τF ≡ intrinsic delay [s]

τF is overall time constant for minority carrier storage in BJT in

FAR:

τtEτF = + τtB

βF

Note: emitter contribution to τF is τtE/βF because IB is βF times

smaller than IC .

If VBE changes, QE and QB change ⇒ capacitive effect:

dQF qICCF = = τF

dVBE kT



Location of this capacitance? Think of which terminals supply stored

charge (minority and majority carriers):

For QE:

• minority carriers (holes) injected from base

• majority carriers (electrons) come from emitter contact

For QB:

• minority carriers (electrons) injected from emitter

• majority carriers (holes) come from base contact

Equivalent-circuit model:

C

QjC

E

IS

βF

qVBE(exp -1)kT

QjE

qVBEIS expB kT

QF


�


Similar picture in reverse regime: charge storage in base and collector

QR = τRIE

τR a bit complicated because it accounts for charge storage in in

trinsic and extrinsic base and collector regions.

B E B

C


charge in�

base QNR�


charge in�

collector QNR

Diffusion capacitance:

dQR qIECR = = τR

dVBC kT

Located between base and collector terminals.



By superposition, complete equivalent circuit model valid in all four

regimes:

C

B

IS

βF

qVBE(exp kT

-1)

QjCQR

QjEQF

IS

βR

qVBC(exp kT

-1)

qVBE qVBCIS (exp - exp )kT kT

E



3. Small-signal behavior of ideal BJT

In analog (and digital) applications, interest in behavior of BJT to

small-signal applied on top of bias

⇒ small-signal equivalent circuit model.

� Small-signal equivalent circuit model in FAR

Must linearize hybrid-π model in FAR:

C

QjC

E

IS

βF

qVBE(exp -1)kT

QjE

qVBEIS expB kT

QF

-Non-linear voltage-controlled current source linearized to linear voltage

controlled current source.

-Diode linearized to resistor.

-Charge storage elements linearized to capacitors.



• Linearized voltage-controlled current source

Apply small signal vbe on top of bias VBE. n

nB(VBE)

WB

IC

nB(VBE+vbe)

IC+ic

nB(WB)=0

0 x

Collector current:

q(VBE + vbe) qVBE qvbe qvbe IC+ic = IS exp � IS exp (1+ ) = IC(1+ )

kT kT kT kT

Small-signal collector current:

qICic = vbe

kT

Define transconductance:

qIC gm =

kT

gm depends only on absolute value of IC and T (unlike MOSFET,

where gm depends on device geometry)



• Linearized diode p

pE(VBE+vbe)

pE(VBE) IB+ib

ni2

NE

IB

-WE-xBE -xBE x

Base current:

q(VBE + vbe) IS qVBE qvbe IB + ib = IS exp � exp (1 + )

kT βF kT kT

Small-signal base current:

qIBib = vbe

kT

Define conductance:

qIB q IC gm gπ = = =

kT kT βF βF

Then, in general,

gπ � gm



• Capacitors

QjE → Cje

QjC → Cjc

qICQF → Cπ = τF

kT

Two components in Cπ:

nBpE

-xBE

pE(VBE)

IB

ΔQB pE(VBE+vbe) ΔQE

nB(VBE+vbe)

IB+ib

IC+ic

ni2 nB(WB)=0

NE

-WE-xBE x 0 x

nB(VBE)

WB

IC

Note:

Cπ = τFgm



• Small-signal equivalent circuit model for ideal BJR in FAR:

Cjc

CB +

vbe gmvbeCπ+Cje gπ

E



Key conclusions

• In BJT, two types of stored charge: depletion layer charge and

minority carrier charge.

• Depletion layer charge accounted through depletion capacitances.

• Minority carrier charge accounted through time constant τF (in

trinsic delay):

τtE τF = + τtB

βF

Emitter contribution to τF is βF times smaller than τtE because

IB is βF times smaller than IC.

• Non-linear hybrid-π model for ideal BJT including charge stor

age elements:

C

B

IS

βF

qVBE(exp kT

-1)

QjCQR

QjEQF

IS

βR

qVBC(exp kT

-1)

qVBE qVBCIS (exp - exp )kT kT

E



• Small-signal equivalent circuit model of ideal BJT in FAR:

Cjc

E

CB +

vbe gmvbeCπ+Cje gπ

with:

qIC qIB gm gm = gπ = = Cπ = τFgm

kT kT βF


Documents

May 4, 2007 1. Current-voltage characteristics of ideal ... · B E B B E B depletion charge in base-emitter SCR depletion charge in base-collector SCR C minority carrier charge in