EE 434Lecture 22

Bipolar

Device Models

Quiz 14

The collector current of a BJT was measured to be 20mA and the base current measured to be 0.1mA. What is the efficiency of injection of electrons coming from the emitter to the collector?

IC

IB

And the number is ….

631

24578

9

And the number is ….

631

24578

9

1

Quiz 14

The collector current of a BJT was measured to be 20mA and the base current measured to be 0.1mA. What is the efficiency of injection of electrons coming from the emitter to the collector?

IC

IBSolution:

2001.

20

mA

mA

B

C

I

Iβ

α1

αβ

Efficiency = α

β1

βα

.9952001

200α

– Bipolar device operation dependent upon how minority carriers in base contribute to collector current

– Bipolar model (in high gain region)• Diode model for BE junction, injection efficiency for IC α

– Bipolar transistor is inherently a current amplifier with exponential relationship between collector current and VBE

• This property makes BJT very useful

Review from Last Time

t

BE

V

V

C eI SI~

t

BE

V

V

B eI SI~

t

BE

V

V

C eI SI~

CB IIβ

1

Bipolar Models

Simple dc Model

Small SignalModel

Frequency-Dependent Small Signal Model

Better Analytical dc Models

Sophisticated Model for Computer Simulations

Better Models for Predicting

Device Operation

Bipolar Models

Simple dc Model

Small SignalModel

Frequency-Dependent Small Signal Model

Better Analytical dc Models

Sophisticated Model for Computer Simulations

Better Models for Predicting

Device Operation

Bipolar ModelsSimple dc Model

IC C

E

BIB

VBE

VCE

following convention, pick IC and IB as dependent variables and VBE and VCE as independent variables

Simple dc modelIC C

E

BIB

VBE

VCE

t

BE

V

V

B eI SI~

t

BE

V

V

C eI SI~

qkT

Vt

From last time :

This has the properties we are looking for but the variables we usedin introducing these relationships are not standard

SI~

It can be shown that is proportional to the emitter area AE

Define and substitute this into the above equations ESAJ1~ SI

Simple dc model

t

BE

V

V

B eI SI~

t

BE

V

V

C eI SI~

qkT

Vt

t

BE

V

V

ESB e

βAJ

I

t

BE

V

V

ESC eAJI

qkT

Vt

JS is termed the saturation current density

Process Parameters : JS,β

Design Parameters: AE

Environmental parameters and physical constants: k,T,q

At room temperature, Vt is around 26mV

JS very small – around .25fA/u2

Transfer CharacteristicsJS=.25fA/u2

AE=400u2

VBE close to 0.6V for a two decade change in IC around 1mA

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.1 1 10

IC (mA)

VB

E

Transfer CharacteristicsJS=.25fA/u2

AE=400u2

VBE close to 0.6V for a four decade change in IC around 1mA

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.001 0.01 0.1 1 10 100 1000

IC (mA)

VB

E

Simple dc model

0

50

100

150

200

250

300

0 1 2 3 4 5

Vds

IdIC

VCE

VBE or IB

t

BE

V

V

ESC eAJI

Output Characteristics

Simple dc model

0

50

100

150

200

250

300

0 1 2 3 4 5

Vds

IdIC

VCE

VBE or IB

Better Model of Output Characteristics

Simple dc model

VBE or IB

Typical Output Characteristics

0

50

100

150

200

250

300

0 1 2 3 4 5

Vds

Id

IC

VCE

Forward ActiveSaturation

Cutoff

Forward Active region of BJT is analogous to Saturation region of MOSFET

Saturation region of BJT is analogous to Triode region of MOSFET

Simple dc model

VBE or IB

Typical Output Characteristics

0

50

100

150

200

250

300

0 1 2 3 4 5

Vds

Id

IC

VCE

Projections of these tangential lines all intercept the –VCE axis at the same place and this is termed the Early voltage, VAF (actually –VAF is intercept)

Typical values of VAF are in the 100V range

Simple dc model

VBE or IB

Improved Model

0

50

100

150

200

250

300

0 1 2 3 4 5

Vds

Id

IC

VCE

AF

CEV

V

SC VV

1eJI t

BE

t

BE

V

V

ESB e

βAJ

I Valid only in Forward Active Region

Simple dc model

VBE or IB

Improved Model

0

50

100

150

200

250

300

0 1 2 3 4 5

Vds

Id

IC

VCE

Valid in All regions of operation

11 t

BC

t

BE

V

V

SV

V

F

SE eJe

JI E

E AA

11 t

BC

t

BE

V

V

SV

V

SC eJ

eJIR

EE

AA

qkT

Vt

Not mathematically easy to work withNote dependent variables changes

Termed Ebers-Moll model

VAF effects can be added

Reduces to previous model in FA region

Simple dc model

11 t

BC

t

BE

V

V

SV

V

F

SE eJe

JI E

E AA

11 t

BC

t

BE

V

V

SV

V

SC eJ

eJIR

EE

AA

qkT

Vt

Ebers-Moll model

Process Parameters: {JS, αF, αR}

Design Parameters: {AE}

αF is the parameter α discussed earlierαR is termed the “reverse α”

F

F

F

αβ =

1-αR

R

R

αβ =

1-α

JS ~10-16A/μ2 βF~100, βR~0.4

Typical values for process parameters:

Completely dominant!

Simple dc model

11 t

BC

t

BE

V

V

SV

V

F

SE eJe

JI E

E AA

11 t

BC

t

BE

V

V

SV

V

SC eJ

eJIR

EE

AA

qkT

Vt

Ebers-Moll model

JS ~10-16A/μ2 βF~100, βR~0.4

With typical values for process parameters in forward active region (VBE~0.6V, VBC~-3V), with Vt=26mV and if AE=100μ2:

11 t

BC

t

BE

V

V

SV

V

SC eJ

eJIR

EE

AA

1410 1 128

-14

10 -51

C

10I 1.05x10 7.7x10

.

Makes no sense to keep anything other thanBE

t

V

V

C SI J e

EA

in forward active

Simple dc model

11 t

BC

t

BE

V

V

SV

V

F

SE eJe

JI E

E AA

11 t

BC

t

BE

V

V

SV

V

SC eJ

eJIR

EE

AA

qkT

Vt

Ebers-Moll model

Alternate equivalent expressions for dependent variables {IC, IB} defined earlier for Ebers-Moll equations in terms of independent variables {VBE, VCE}

1CEBE

t t

-VV

V VR

C S E

R

1+βI J A e e

β

CEBE

t t

-VV

V V

B S E

F R

1 1I J A e - e

β β

No more useful than previous equation but in form consistent with notation Introduced earlier

Simple dc modelSimplified Multi-Region Model

IC

VCE

VBE1

VBE2

VBE3

VBE4

VBE5

IC

VCE

VBE1

VBE2

VBE3

VBE4

VBE5

VCESAT

Ebers-Moll Model Simplified Multi-Region Model

1CEBE

t t

-VV

V V CER

C S E

R AF

V1+βI J A e e 1+

β V

AF

CEV

V

ESC V

V1eAJI t

BE

VBE=0.7VVCE=0.2V

IC=IB=0

CEBE

t t

-VV

V V

B S E

F R

1 1I J A e - e

β β

t

BE

V

V

ESB e

βAJ

I

Forward Active

Saturation

Cutoff

Simple dc modelSimplified Multi-Region Model

AF

CEV

V

ESC V

V1eAJI t

BE

t

BE

V

V

ESB e

βAJ

I

q

kTVt

VBE=0.7VVCE=0.2V

IC=IB=0

Forward Active

Saturation

Cutoff

Simple dc modelSimplified Multi-Region Model

AF

CEV

V

ESC V

V1eAJI t

BE

t

BE

V

V

ESB e

βAJ

I

q

kTVt

VBE=0.7VVCE=0.2V

IC=IB=0

Forward Active

Saturation

Cutoff

VBE>0.4V

VBC<0

IC<βIB

VBE<0

VBC<0

A small portion of the operating region is missed with this model but seldom operate in the missing region

Simple dc modelEquivalent Simplified Multi-Region Model

AF

CEBC V

V1βII

t

BE

V

V

ESB e

βAJ

I

q

kTVt

VBE=0.7VVCE=0.2V

IC=IB=0

Forward Active

Saturation

Cutoff

VBE>0.4V

VBC<0

IC<βIB

VBE<0

VBC<0

A small portion of the operating region is missed with this model but seldom operate in the missing region

Bipolar Models

Simple dc Model

Small SignalModel

Frequency-Dependent Small Signal Model

Better Analytical dc Models

Sophisticated Model for Computer Simulations

Better Models for Predicting

Device Operation