6.012 microelectronic devices and circuits, lecture 18 · saturation -the flux picture both...

• Large-signal equivalent circuit model

Lecture 18The Bipolar Junction Transistor (II)

Regions of Operation

Outline

• Regions of operation

• Large-signal equivalent circuit model

• Output characteristics

Reading Assignment: Howe and Sodini; Chapter 7, Sections 7.3, 7.4 & 7.5

6.012 Spring 2009 Lecture 18 1

1.  BJT: Regions of Operation

VBE

C- +

forward� saturation VBC active

+ B VCE

+ VBC

VBE reverse - cut-off -

E

• Forward active: device has high voltage gain and

high β;

• Reverse active: poor β; not useful;

• Cut­off: negligible current: nearly an open circuit;

• Saturation: device is flooded with minority

carriers;

– ⇒ takes time to get out of saturation

6.012 Spring 2009 Lecture 18 2

Minority Carrier profiles (not to scale):

Forward­Active Region: VBE > 0, VBC <0

n-Emitter p-Base n-Collector

IE<0

IB>0

IC>0

VBE > 0 VBC < 0

Minority Carrier profiles (not to scale):

npB pnE pnC

npBo pnEo

pnCo

0 WB-XBE WB+XBC -WE-XBE WB+XBC+WC

x

emitter base collector

6.012 Spring 2009 Lecture 18 3

• Emitter current:

Forward­Active Region: VBE > 0, VBC < 0

• Emitter injects electrons into base, collector extracts

(collects) electrons from base:

IC = ISe VBE Vth[ ]

; IS = qAEnpBo Dn

WB

• Base injects holes into emitter, holes recombine at

emitter contact:

IB = IS ββββF

e VBE Vth[ ]− 1

;

IS ββββF

= qAE pnEoDp

WE

• Emitter current:

IE = −IC − IB = −ISe VBE Vth[ ]−

IS ββββF

e VBE Vth[ ]−1

• State-of-the-art IC BJT’s today: IS ≈ 0.1 - 1 fA

• βF ≈ 50 - 300.

• βF hard to control tightly: ⇒ circuit design techniques

required to be insensitive to variations in βF.

βF = IC

IB

= npBo •

D n WB

pnEo • D p WE

= NdE D n WE

NaB D p WB

6.012 Spring 2009 Lecture 18 4

Reverse­Active Region: VBE < 0, VBC > 0

n-Emitter p-Base n-Collector

IE>0

IB>0

IC<0

VBE < 0 VBC > 0

Minority Carrier Profiles (not to scale):

npB pnE pnC

npBo pnEo

pnCo

0 WB-XBE WB+XBC -WE-XBE WB+XBC+WC

x

emitter base collector

6.012 Spring 2009 Lecture 18 5

• Collector current:

Reverse­Active Region: VBE < 0, VBC > 0

• Collector injects electrons into base, emitter extracts

(collects) electrons from base:

IE = ISe VBC Vth[ ]

; IS = qACnpBoDn

WB

• Base injects holes into collector, holes recombine at

collector contact and buried layer:

IB = IS ββββR

e VBC Vth

( )−1

;

IS ββββR

= qAC pnCoDp

WC

• Collector current:

IC = −IE − IB = −ISe VBC Vth[ ]−

IS ββββR

e VBC Vth[ ]−1

• Typically, βR ≈ 0.1 - 5 << βF .

βR = IE

IB

= npBo •

D n WB

pnCo • D p WC

= NdC D n WC

NaB D p WB

6.012 Spring 2009 Lecture 18 6

Cut­Off Region: VBE < 0, VBC < 0

n-Emitter p-Base n-Collector

IE>0

IB<0

IC>0

VBE < 0 VBC < 0

Electrons flow only if

Generation occurs

Minority Carrier Profiles (not to scale):

npB pnE pnC

npBo pnEo

pnCo

0 WB-XBE WB+XBC -WE-XBE WB+XBC+WC

x

emitter base collector

6.012 Spring 2009 Lecture 18 7

• These are tiny leakage currents (≈10 A).-

Cut­Off Region: VBE < 0, VBC < 0

• Base extracts holes from emitter:

IB1 = − IS = −IEββββF

• Base extracts holes from collector:

IB2 = − IS = −ICββββR

-15 • These are tiny leakage currents (≈10 15 A).

6.012 Spring 2009 Lecture 18 8

Saturation Region: VBE > 0, VBC > 0

n-Emitter p-Base n-Collector

IE

IB<0

IC

VBE > 0 VBC > 0

IB>0

Minority Carrier profiles (not to scale):

npB pnE pnC

npBo pnEo

pnCo

0 WB-XBE WB+XBC -WE-XBE WB+XBC+WC

x

emitter base collector

6.012 Spring 2009 Lecture 18 9

E S = th th S th

Saturation Region: VBE > 0, VBC > 0

Saturation is superposition of forward active + reverse

active: [VBE ] [VBC ] IS

[VBC ] IC = IS

e

Vth − e Vth − ββββR

e

Vth − 1

IS [VBE ]

IS [VBC ]

IB = e Vth − 1 + e Vth − 1 ββββF

ββββR

[VBE ] [VBC ] IS

[VBE ] VthI = −I e Vth − e Vth − e −1IE −IS e

[ ]− e[ ]

−

ββββF e[ ]−1

• IC and IE can have either sign, depending on relative

magnitudes of VBE and VBC and βF and βR.

6.012 Spring 2009 Lecture 18 10

Saturation - The Flux Picture Both junctions are injecting and collecting. Electrons injected from emitter into base are collected by the collector as in Forward Active case. Electrons injected from collector into the base are collected by the emitter as in Reverse Active case. Holes injected into emitter recombine at ohmic contact as in Forward Active case. Holes injected into collector recombine with electrons in the n+ buried layer

6.012Spring 2009 Lecture 18

Equivalent-circuit model representation (non­linear

2. Large­signal equivalent circuit model

System of equations that describes BJT operation:

IC = IS e VBE Vth[ ]

− e VBC Vth[ ]

−

IS ββββR

e VBC Vth[ ]

− 1

IB = IS ββββF

e VBE Vth[ ]− 1

+

IS ββββR

e VBC Vth[ ]− 1

IE = −IS e VBE Vth[ ]− e

VBC Vth[ ]

−

IS ββββF

e VBE Vth[ ]−1

Equivalent-circuit model representation (non­linear hybrid­π model) [particular rendition of Ebers-Moll

model in text]:

Three parameters in this model: IS, βF, and βR.

B

C

E

IB

IR

IF

IS/βR

IS/βF

IE

IC

βFIF - βRIR

=IS[exp(qVBE/kT) - exp(qVBC/kT)]+

-

+

-

VBE

VBC

6.012 Spring 2009 Lecture 18 12

Simplification of equivalent circuit model: • Forward­active region: VBE > 0, VBC < 0

For today’s technology: VBE,on ≈ 0.7 V. IB depends on

outside circuit.

B

C

E

B

C

E

VBE,on

ISe VBE Vth

[ ]

• Reverse­active region: VBE < 0, VBC > 0

For today’s technology: VBC,on ≈ 0.6 V

B

C

E E

B

C

VBC,on

ISe VBC Vth

[ ]

6.012 Spring 2009 Lecture 18 13

Simplification of equivalent circuit model: • Saturation region: VBE > 0, VBC > 0

For today’s technology: VCE,sat ≈ 0.1 V. IC and IB depend

on outside circuit.

B

C

E

B

C

E

VBE,on VBE,on

VCE,sat

VBC,on VBC,on

B

C

E

+

-

6.012 Spring 2009 Lecture 18 14

• Cut­off region: VBE < 0, VBC < 0

on outside circuit.

Only negligible leakage currents.

B

C

E

I =0

3. Output Characteristics

Common­emitter output characteristics:

IC

IB

IB=0

6.012 Spring 2009 Lecture 18 15

VCE=VCB+VBE

VCE,sat

B

0 0

Common­Emitter Output Characteristics

6.012 Spring 2009 Lecture 18 16

What did we learn today? Summary of Key Concepts

• Forward­active region: For bias calculations:

• Saturation Region: For bias calculations:

B C

E

VBE,on

C

+

ISe VBE Vth[ ]

6.012 Spring 2009 Lecture 18 17

• Cut­off Region: For bias calculations:

VBE,on

VCE,sat

VBC,on

B

E

-

B

C

E

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6.012 Microelectronic Devices and Circuits Spring 2009

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