EE 434Lecture 22

Bipolar Device Models

Quiz 14The 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?

And the number is ….

631

24578

9

And the number is ….

631

24578

9

Quiz 14The 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?

Solution:

2001.

20===

mAmA

B

C

IIβ

α1αβ−

=

Efficiency = α

β1βα+

=

.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

BEV

V

C eI SI~β=

t

BEV

V

B eI SI~=

t

BEV

V

C eI SI~β=

CB IIβ1

=

Bipolar Models

Simple dc Model

Small SignalModel

Frequency-Dependent Small Signal Model

Better Analytical dc Models

Sophisticated Model for Computer Simulations

Better Modelsfor 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 Modelsfor Predicting

Device Operation

Bipolar ModelsSimple dc Model

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

Simple dc model

t

BEV

V

B eI SI~=

t

BEV

V

C eI SI~β=

qkTVt =

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~ −= βSI

Simple dc model

t

BEV

V

B eI SI~=

t

BEV

V

C eI SI~β=

qkTVt =

t

BE

VV

ESB e

βAJI =

t

BE

VV

ESC eAJI =

qkTVt =

JS is termed the saturation current density

Process Parameters : JS,β

Design Parameters: AE

Environmental parameters and physical constants: k,T,qAt room temperature, Vt is around 26mVJS 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)

V BE

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)

V BE

Simple dc model

0

50

100

150

200

250

300

0 1 2 3 4 5

Vds

IdIC

VCE

VBE or IB

t

BE

VV

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

CEVV

SC VV1eJI t

BE

t

BE

VV

ESB e

βAJI =

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

VV

SV

V

F

SE eJeJI E

E AAα

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−= 11 t

BC

t

BE

VV

SVV

SC eJeJIR

EE

AAα

qkTVt =

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

VV

SV

V

F

SE eJeJI E

E AAα

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−= 11 t

BC

t

BE

VV

SVV

SC eJeJIR

EE

AAαq

kTVt =

Ebers-Moll model

Process Parameters: {JS, αF, αR}

Design Parameters: {AE}

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

FF

F

αβ =1-α

RR

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

VV

SV

V

F

SE eJeJI E

E AAα

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−= 11 t

BC

t

BE

VV

SVV

SC eJeJIR

EE

AAαq

kTVt =

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

VV

SVV

SC eJeJIR

EE

AAα

( ) ( )1410 1 128

-1410 -51

C

10I 1.05x10 7.7x10.

−= − − −

Makes no sense to keep anything other thanBE

t

VV

C SI J e

EA ⎛ ⎞= ⎜ ⎟⎝ ⎠

in forward active

Simple dc model

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−−= 11 t

BC

t

BE

VV

SV

V

F

SE eJeJI E

E AAα

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−= 11 t

BC

t

BE

VV

SVV

SC eJeJIR

EE

AAαq

kTVt =

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

-VVV VR

C S E

R

1+βI J A e eβ

⎛ ⎞⎡ ⎤= −⎜ ⎟⎢ ⎥

⎣ ⎦⎝ ⎠CEBE

t t

-VVV V

B S E

F R

1 1I J A e - eβ β⎛ ⎞

= ⎜ ⎟⎝ ⎠

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

Simple dc modelSimplified Multi-Region Model

Ebers-Moll Model Simplified Multi-Region Model

1CEBE

t t

-VVV V CER

C S E

R AF

V1+βI J A e e 1+β V

⎛ ⎞⎡ ⎤ ⎛ ⎞= −⎜ ⎟⎜ ⎟⎢ ⎥

⎣ ⎦ ⎝ ⎠⎝ ⎠

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

AF

CEVV

ESC VV1eAJI t

BE

VBE=0.7VVCE=0.2V

IC=IB=0

CEBE

t t

-VVV V

B S E

F R

1 1I J A e - eβ β⎛ ⎞

= ⎜ ⎟⎝ ⎠

t

BE

VV

ESB e

βAJI =

Forward Active

Saturation

Cutoff

Simple dc modelSimplified Multi-Region Model

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

AF

CEVV

ESC VV1eAJI t

BE

t

BE

VV

ESB e

βAJI =

qkTVt =

VBE=0.7VVCE=0.2V

IC=IB=0

Forward Active

Saturation

Cutoff

Simple dc modelSimplified Multi-Region Model

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

AF

CEVV

ESC VV1eAJI t

BE

t

BE

VV

ESB e

βAJI =

qkTVt =

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

VV

ESB e

βAJI =

qkTVt =

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