Document 13510624

6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 35-1

Lecture 35 - Bipolar Junction Transistor

(cont.)

May 3, 2007

Contents:

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

Reading material: del Alamo, Ch. 11, § 11.2 (11.2.1)

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].

6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007

Key questions

Lecture 35-2

• How does the BJT operate in other regimes?

• How does a complete model for the ideal BJT look like?




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

� Forward-active regime ( V

BE

> 0 , V

BC

< 0)

Summary of key results: n-Emitter

W

B

<< L

B p-Base n-Collector

I

E

<0 I

C

>0

I

B

>0

V

BE

> 0

I

C

= I

S exp qV

BE kT

V

BC

< 0

I

S

I

B

= (exp

β

F qV

BE kT

− 1)

I

E

= − I

C

− I

B

= − I

S exp qV

BE

I

S

− (exp kT β

F qV

BE kT

− 1)




• Current gain

I

C

β

F

� �

I

B n

2 i

N

B n

2 i

N

E

D

W

B

B

D

E

W

E

=

N

E

D

B

W

E

N

B

D

E

W

B

To maximize β

F

:

Lecture 35-4

• N

E

� N

B

• W

E

� W

B

(for manufacturing reasons, W

E

� W

B

)

• want npn , rather than pnp because this way D

B

> D

E

β

F hard to control ⇒ if β

F is high enough ( > 50), circuit techniques effectively compensate for this.







• Equivalent circuit model

C

Lecture 35-6

B

I

S

β

F

(exp qV

BE kT

-1)

I

S exp qV

BE kT

E

I

C

= I

S exp qV

BE kT

I

S

I

B

= (exp

β

F qV

BE kT

− 1)

I

E

= − I

C

− I

B

= − I

S exp qV

BE

I

S

− (exp kT β

F qV

BE kT

− 1)




• Energy band diagram

E(n) B(p) C(n) thermal� equilibrium

E

C

E

V forward� active

E

C

E

V

E fh

E fe qV

BE qV

BC

E

F

Lecture 35-7

• Summary of minority carrier profiles (not to scale) p

E n

B p

C p

Eo

-W

E

-x

BE

x

BE

0

� n

Bo p

Co

W

B

W

B

+x

BC

W

B

+x

BC

+W

C x




� Reverse regime ( V

BE

< 0 , V

BC

> 0)

I

E

: electron injection from C to B, collection into E

I

B

: hole injection from B to C, recombination in C

Lecture 35-8 n-Emitter p-Base n-Collector

I

E

>0

I

C

<0

I

B

>0

V

BE

< 0

Minority carrier profiles (not to scale) :

V

BC

> 0 p

E n

B p

C p

Eo

-W

E

-x

BE

x

BE

0

� n

Bo p

Co

W

B

W

B

+x

BC

W

B

+x

BC

+W

C x




Current equations (just like FAR, but role of collector and emitter reversed):

I

B

= qV

BC

I

E

= I

S exp

I

S

β

R

(exp kT qV

BC kT

− 1)

I

C

= − I

E

− I

B

= − I

S exp qV

BC kT

−

I

S

β

R

(exp qV

BC kT

− 1)

Equivalent-circuit model representation:

C

I

S

β

R

(exp qV

BC kT

-1)

B I

S exp qV

BC kT

E




Prefactor in I

E expression is I

S

: emitter current scales with A

E

.

B E B B E B

I

E

A

E

I

B

A

C

C C

But, I

B scales roughly as A

C

:

• downward component scales as A

C

• upward component scales as A

C

− A

E

� A

C

Hence, β

R

� 0 .

1 − 5 � β

F

.



6.012 - Microelectronic Devices and Circuits - Fall 2005

Forward-active Gummel plot ( V

CE

= 3 V ):

Lecture 18-8

Reverse Gummel ( V

EC

= 3 V ):




Energy band diagram:

E(n) B(p) thermal� equilibrium

E

C

E

V reverse

E

C

E

V

E fe qV

BC qV

BE

E fh

Lecture 35-11

C(n)

E

F




� Cut-off regime ( V

BE

< 0 , V

BC

< 0)

I

E

: hole generation in E, extraction into B

I

C

: hole generation in C, extraction into B n-Emitter p-Base n-Collector

I

E

>0

I

C

>0

Lecture 35-12

I

B

<0

V

BE

< 0


V

BC

< 0 p

E n

B p

C p

Eo

-W

E

-x

BE

x

BE

0

� n

Bo p

Co

W

B

W

B

+x

BC

W

B

+x

BC

+W

C x




Current equations:

I

S

I

E

=

β

F

I

S

I

S

I

B

= − −

β

F

β

R

I

S

I

C

=

β

R

These are tiny leakage currents ( ∼ 10 − 12 A )

Equivalent-circuit model representation:

C

I

S

β

R

B

I

S

β

F both reverse � biased

E

Lecture 35-13




• Energy band diagram

E(n) B(p) thermal� equilibrium

E

C

E

V

C(n)

Lecture 35-14

E

F cut-off

E

C

E

V qV

BE

E fh

E fe qV

BC




� Saturation regime ( V

BE

> 0 , V

BC

> 0)

I

C

, I

E

: balance of electron injection from E/C into B

I

B

: hole injection into E/C, recombination in E/C, respectively n-Emitter p-Base n-Collector

I

E

I

C

I

B

<0

V

BE

> 0


V

BC

> 0 p

E n

B p

C p

Eo

-W

E

-x

BE

x

BE

0

� n

Bo p

Co

W

B

W

B

+x

BC

W

B

+x

BC

+W

C x




Current equations: superposition of forward active + reverse:

I

I

C

B

=

=

I

I

S

β

F

(exp

I

E

= −

S

(exp

I

S

β

F qV

BE kT qV

BE

− exp

(exp kT qV

− 1) +

BE kT qV

BC

) − kT

I

S

β

R

(exp

− 1) − I

S

(exp

I

S

β

R

(exp qV

BC kT qV

BC kT qV

BE

− 1)

− exp kT

− 1) qV

BC

) kT

I

C and I

E can have either sign, depending on relative magnitude of

V

BE and V

BC and β

F and β

R

.

Equivalent circuit model representation ( Non-Linear Hybridπ Model ):

C

I

S

β

R

(exp qV

BC kT

-1)

B

I

S

β

F

(exp qV

BE kT

-1)

I

S

(exp qV

BE kT

- exp qV

BC kT

)

E

Complete model has only three parameters: I

S

, β

F

, and β

R

.




Energy band diagram:

E(n) B(p) C(n)

Lecture 35-17 thermal� equilibrium

E

C

E

V

E

F saturation

E

C

E

V

E fh qV

BE

E fe qV

BC

In saturation, collector and base flooded with excess minority carriers

⇒ takes lots of time to get transistor out of saturation.




Key conclusions

Lecture 35-18

• In FAR, current gain β

F maximized if N

E

� N

B

.

• β

F hard to control precisely: if big enough ( > 50), circuit tech niques can compensate for variations in β

F

.

• BJT design optimized for operation in forward-active regime ⇒ operation in inverse regime is poor: β

R

� β

F

.

• In saturation, BJT flooded with minority carriers ⇒ takes time to get BJT out of saturation.

• Hybridπ model: equivalent circuit description of BJT in all regimes:

C

I

S

β

R

(exp qV

BC kT

-1)

B

I

S

β

F

(exp qV

BE kT

-1)

I

S

(exp qV

BE kT

- exp qV

BC kT

)

E

• Only three parameters needed to describe behavior of BJT in four regimes: I

S

, β

F

, and β

R

.



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