Session 11: Solid State Physics Bipolar Junction...

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Transcript of Session 11: Solid State Physics Bipolar Junction...

Bipolar Junction Transistor

Session 11: Solid State Physics

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5.

Outline

� A� B

� C

� D

� E

� F� G

� H

� I

� J

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1. I

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5.

Introduction

3

In recent decades, the higher layout density and low-power advantage

of CMOS technology has eroded the BJT’s dominance in integrated-

circuit products.

(higher circuit density � better system performance)

BJTs are still preferred in some integrated circuit applications because

of their high speed and superior intrinsic gain.

� faster circuit speed

� larger power dissipation

� limits device density (~104 transistors/chip)

Si (npn, pnp) � SiGe HBT � GaAs (InSb) HBT

1. I

2.

3.

4.

5.

BJT Types and Definitions

4

Emitter

��

�np+ p-

Collector

Base

The BJT is a 3-terminal device, with two types: PNP and NPN

Emitter

��

�pn+ n-

Collector

Base

Asymmetric!

��� ��

pnp npn

�� ���

��� �

����� �� � ��

�� ���

�� ��

�����

1. I

2.

3.

4.

5.

Review: Current Flow in a

Reverse-Biased pnJunction

5

� In a reverse-biased pn junction, there is negligible diffusion of

majority carriers across the junction. The reverse saturation

current is due to drift of minority carriers across the junction and

depends on the rate of minority-carrier generation close to the

junction (within ~one diffusion length of the depletion region).

⇒ We can increase this reverse current by increasing the rate of

minority-carrier generation, e.g. by

� optical excitation of carriers (e.g. photodiode)

� electrical injection of minority carriers into the vicinity of the

junction…

1. I

2.

3.

4.

5.

PNP BJT Operation (Qualitative)

6

A forward-biased “emitter” pn junction is used to inject minority carriers

into the vicinity of a reverse-biased “collector” pn junction.

� The collector current is controlled via the base-emitter junction

Emitter

�np+ p-Collector

��� ��

�� ���

��� �

����� ��hole

Base

“F” “R”

��

��

� � 0 � � 0

��� ������ ���

� ≡ ���To achieve high current gain:

• The injected minority carriers should not recombine within the quasi-neutral

base region

• The emitter junction current is comprised almost entirely of carriers injected

into the base (rather than carriers injected into the emitter)

1. I

2.

3.

4.

5.

Base Current Components

(Active Mode of Operation)

7

The base current consists of majority carriers supplied for

1. Recombination of injected minority carriers in the base

2. Injection of carriers into the emitter

3. Reverse saturation current in collector junction (Reduces |�|)4. Recombination in the base-emitter depletion region

Emitter

�np+ p-Collector

��� ��

�� ���

��� �

����� ��hole

Base

“F” “R”

��

��

� � 0 � � 0

��� ������ ���

� ≡ ���

1. I

2.

3.

4.

5.

BJT Circuit Configurations

8

���

��� � 010��20��30��

Output Characteristics for Common-Emitter Configuration

CE: Common EmitterCB: Common Base CC: Common Collector

1. I

2.

3.

4.

5.

BJT Modes of Operation

9

p n p n p n

21E C

B

21E C

B

Qn

E

C

B

B

E

Qp

VBE

VBC

1 : F

2 : R

1 : F

2 : F

1 : R

2 : F1 : R

2 : R

SaturationActive

ReversedCut-Off

1. I

2.

3.

4.

5.

BJT Electrostatics

10

Under normal operating conditions, the BJT may be viewed electrostatically as

two independent pn junctions

������� �

Emitter

np+ p-

CollectorBase

pnp

1. I

2.

3.

4.

5.

BJT Electrostatics

11

Under normal operating conditions, the BJT may be viewed electrostatically as

two independent pn junctions

������� �

Emitter

np+ p-

CollectorBase

pnp

1. I

2.

3.

4.

5.

BJT Electrostatics

12

������� �

Emitter

np+ p-

CollectorBasepnp

� �

!�!�

"

"

1. I

2.

3.

4.

5.

BJT Electrostatics

13

#

Emitter

np+ p-

CollectorBasepnp

� �""

$

1. I

2.

3.

4.

5.

BJT Performance Parameters (PNP)

14

Emitter

�np+ p-Collector

�hole

Base

“F” “R”

��

���

� � 0 � � 0��� ������ ��� % ≡ ������ � ��

!�!�

Emitter Efficiency:

&' ≡ ������Base Transport Factor:

&() ≡ %&'Common-Base d.c. Current Gain:

1 2345

5 ↘ relative to 1 � 2

1 ↘ relative to 2

1. I

2.

3.

4.

5.

Collector Current (PNP)

15

Emitter

�np+ p-Collector

�hole

Base

“F” “R”

��

���

� � 0 � � 0��� ������ ���

!�!�

The collector current is comprised of:2 Holes injected from emitter, which do

not recombine in the base 3 Reverse saturation current of collector

junction

where ��. is the collector current

which flows when �� / 0

1 2345

�� / &()�� � ��.

�� / &() �� � � � ��.�� / &()1 � &() � � ��.1 � &()/ �� � ���.

1. I

2.

3.

4.

5.

Notation (PNP BJT) , Assumptions

16

0

Emitter

np+ p-

CollectorBase

� �"0" 0′0′0′′0′′

Assumptions:

1) 1-D structure

2) " ≪ 34 and is constant

3) Like diode gen-rec in depletion region is negligible

4) Uniform doping + step junction

5) Low-level injection everywhere!

Notations:

5 � / 5�67� / 6�3 � / 3�8 � / 8�9�:� / 9�:

5� / 56; / 63� / 38� / 8< := / <:

5 � / 5�67� / 6�3 � / 3�8 � / 8�9�:> / 9�:

≫ �

1. I

2.

3.

4.

5.

“Game Plan” for I-V Derivation

17

0

Emitter

np+ p-

CollectorBase

� �"0" 0′0′0′′0′′

minority-carrier diffusion equation (different set of B.C. for each region)

currents

5�6� 9�: 56 <: 5�6� 9�:

minority-carrier diffusion currents at depletion region edges

0′0 "0′′ 0′′ 0′@� A0BBC

@��A0C@�

0′′@� A0BC

@��A"C@�

�� / �!�5 D∆<D0 FGH: � !�5� D∆9�D0′′ FGBBH:BB�� A0BBC���A0C

�� / �!�5 D∆<D0 FGHI � !�5� D∆9�D0′′ FGBH:B�� A0BC���A"C

9�A0′′C<A0C

9�A0′C

1. I

2.

3.

4.

5.

Minority Carriers

18

0

Emitter

np+ p-

CollectorBase

� �"0" 0′0′0′′0′′

Carriers:

5�6� 9�: 56 <: 5�6� 9�:

Steady-State solution is: DJ∆9�D0J / ∆9�5 8 3 / 5 8 ∆9� 0BB / �KLGBB M�⁄ � �JLOGBB M�⁄

∆< 0 / �KLG M=⁄ � �JLOG M=⁄∆9� 0BB / �KLGB M>⁄ � �JLOGB M>⁄

∆< 0 / <:ALP��= Q'⁄ � 1C∆< " / <:ALP�>= Q'⁄ � 1C∆9� 0′′ / 9�:ALP��= Q'⁄ � 1C

∆9� " / 9�:ALP�>= Q'⁄ � 1C

1. I

2.

3.

4.

5.

Minority Carriers –Active

19

0

Emitter

np+ p-

CollectorBase

� �"0" 0′0′0′′0′′

5�6� 9�: 56 <: 5�6� 9�:

0′0 "0′′ 0′′ 0′9�A0BBC

< 0

0′′<: < " 9�A0BC9�:

9�:

Active: forward reverse

1. I

2.

3.

4.

5.

Minority Carriers –Saturation

20

0

Emitter

np+ p-

CollectorBase

� �"0" 0′0′0′′0′′

5�6� 9�: 56 <: 5�6� 9�:

0′0 "0′′ 0′′ 0′9�A0BBC

< 0

0′′<:

< " 9�A0BC

9�:9�:

Saturation: forward forward

1. I

2.

3.

4.

5.

Minority Carriers –Cut-off

21

0

Emitter

np+ p-

CollectorBase

� �"0" 0′0′0′′0′′

5�6� 9�: 56 <: 5�6� 9�:

0′0 "0′′ 0′′ 0′9�A0BBC < 0

0′′<:

< " 9�A0BC9�:9�:

Cut-off: reverse reverse

1. I

2.

3.

4.

5.

Ideal BJT!

22

0

Emitter

np+

CollectorBase� " 0"0′′0′′�np+ p-

�hole

Base

“F” “R”

���

����� ������ ���

1 2345

" ≪ 3 ( 1 / 0)∆< 0 / �KLG M=⁄ � �JLOG M=⁄ ≅ �KB � �JB0

0 "

< 0

<: < "∆< 0 / <:ALP��= Q'⁄ � 1C∆< " / <:ALP�>= Q'⁄ � 1C

∆< 0 / ∆< 0 � ∆< 0 � ∆< "" 0Swhere

1. I

2.

3.

4.

5.

Current Equations - IE

23

0

Emitter

np+

CollectorBase� " 0"0′′0′′

0 "

< 0

<: < "0′′ 0′′9�A0BBC9�:

���A0′′C / �!�5� D∆9�D0′′ FGBBH:BB/ �!�5�3� 9�: LP��= Q'⁄ � 1���A0C / �!�5 D∆TD0 FGH:/ !�5" ∆< 0 � ∆< "

/ !�5" <: LP��= Q'⁄ � 1 � ALP�>= Q'⁄ � 1C

/ !� 5<:" �5�9�:3� LP��= Q'⁄ � 1 � !�5<:" ALP�>= Q'⁄ � 1C�� / ��� 0 � �� 0BB /

Dominant term

���A0′′C→���A0C→

1. I

2.

3.

4.

5.

Current Equations – IC , IB

24

p-

CollectorBase �" 0" 0′0′

"

0

< "

��� 0 / ��� "→

0′9�A0BC9�:

0′

���A"C →���A0′C

No recombination in Base

�� A0BC / �!�5�9�:3� ALP�>= Q'⁄ � 1C�� / ��� " � �� 0B

�!� 5�9�:3� � 5<:3 ALP�>= Q'⁄ � 1C/ !�5<:" LP��= Q'⁄ � 1

�np+ p-

�hole

Base

“F” “R”

���

����� ������ ���

1 2345

� / �� � �� / !�59�:3� LP��= Q'⁄ � 1 � !�5�9�:3� ALP�>= Q'⁄ � 1CV

W usually >

1. I

2.

3.

4.

5.

Considering Recombination in Base

25

0 "

< 0

<: < "���A0C→ ���A0C→

∆< 0 / �KLG M=⁄ � �JLOG M=⁄ ∆< 0 / <:ALP��= Q'⁄ � 1C∆< " / <:ALP�>= Q'⁄ � 1CS

∆< 0 / <:ALP��=Q' � 1C sinhIOGM=sinh IM= � <:ALP�>=Q' � 1C sinh GM=sinh IM=�� / !� 5�9�:3� � 5<:3 coth IM= LP��=Q' � 1 � !�5<:3 ALP�>=Q' � 1C 1sinh IM=�� / !�5<:3 ALP��=Q' � 1C 1sinh IM= � !� 5<:3 coth IM= � 5�9�:3� ALP�>=Q' � 1C� / �� � ��

1. I

2.

3.

4.

5.

Quasi-Ideal BJT!

26

0 "

< 0

<: < "→ ���A0C→���A0C

→ 4

�J / ∆�8 / !�8 _ ∆< 0 D0I:

/ !�28" ∆< 0 � ∆< "/ !�"<:28 ALP��=Q' � 1C � ALP�>=Q' � 1C

Valid for all regions of operation!

Hence:

�� / ��`(abc�� / ��`(abc � �J� / �`(abc � �J�defgh / !�59�:3� LP��=Q' � 1 � !�5�9�:3� ALP�>=Q' � 1C

� / !� 59�:3� �"<:28 LP��=Q' � 1 � !� 5�9�:3� �"<:28 ALP�>=Q' � 1C~4 j 10V ~7.5 j 10V 4 5

1. I

2.

3.

4.

5.

Quasi-Ideal BJT!

27

Hence:

�� ≅ ��`(abc�� ≅ ��`(abc� ≅ �`(abc � �J

� / !� 59�:3� �"<:28 LP��=Q' � 1 � !� 5�9�:3� �"<:28 ALP�>=Q' � 1C~4 j 10V ~7.5 j 10V 4 5

�� / !� 5<:" �"<:28 LP��=Q' � 1 � !� 5�9�:3� �"<:28 ALP�>=Q' � 1C~7.5 j 10V~7 j 10m

1. I

2.

3.

4.

5.

CB: Common Base

28

Output Characteristic Input Characteristic

��

��

���

���� / 01n�2n�3n�

�0.4Sa

tura

tio

n Active

Cut-Off

��.

Ideal:

very little

dependence to

output voltage

����+

-

����

+

-

&' / 1

np+ p-

��.

→ &()/ ���� / % / ����� / 5<:"5<:" �5�9�:3�/ 11 � 5�5 6;67� "3�⇈

Non ideal: &' / ������ / 1cosh IM=≅ 11 � KJ IM= p → &()/ &'%

Leakage current of BC diode

Determined by 9�: as 9�: ≫ <: np+ p-

��.

1. I

2.

3.

4.

5.

29

1. I

2.

3.

4.

5.

CE: Common Emitter

30

B+

- ���+

-

Output Characteristic Input Characteristic

��

���

�� Saturation Active

Cut-Off0.2

�� / 0�� � 0

very little

dependence to

output voltage

n

p+

p-��� ��

� / 010��20��30��

���.

�� � !�5<:" LP��=Q'" ≪ 3_�� � 0� � 0 r → S � � !�5�9�:3� LP��=Q' → �() / ��� / 55� ∙ <:9�: ∙ 3�"67�6; ⇈⇊

1. I

2.

3.

4.

5.

ICEO and ICBO

31

np+ p-

��.

n

p+

p-

���.���. ≫ ��.

n

p+

p-

���.

���������

��

���. / ��� � ��� / ��. � �()��.

1. I

2.

3.

4.

5.

Ebers-Moll Equations

32

0 "

u<∆<�

∆<�

0 "

u<∆<�

0 "

u<∆<�

Normal Inverted

��v ��v��w ��w ��w � 0��w � 0

∆T� / 0 Normal ��x / y∆<�; ��x / {∆<�∆T� / 0 Inverted ��| / �{∆<� ; ��| / �y∆<� Sy / !�;=M= coth IM={ / !�;=M= csch IM=}�� / ��x � ��| / y∆<� � {∆<��� / ��x � ��| / {∆<� � y∆<�

~��x / ��� LP��=Q' � 1 ; ∆<� / 0��| / ��� 1 � LP�>=Q' ; ∆<� / 0

~�� / ��� LP��=Q' � 1 �&|��|�� / &x�� � ��� LP�>=Q' � 1&x ≡ ��x ��v⁄&| ≡ ��| ��w⁄

1. I

2.

3.

4.

5.

Ebers-Moll Equations

33

~�� / ��� LP��=Q' � 1 �&|��|�� / &x�� � ��� LP�>=Q' � 1~�� / &|��| � ��. LP��=Q' � 1 �� / &x�� � ��. LP�>=Q' � 1

��. LP��=Q' � 1E C

B

& �

��. LP�>=Q' � 1

&����

�� ��� ��

1. I

2.

3.

4.

5.

Charge Control Analysis

34

Normal Inverted

��v ��v ��w ��w��v ≡ �x8�v

�� / ��v � ��w / �x 18�v � 18�v � �|8�w

�� / �x8�v � �| 18�w � 18�w&x ≡ ��x ��v⁄ &| ≡ ��| ��w⁄

�x �|��w ≡ � �|8�w��v / ��v � �x8�v ��w / ��w � �|8�w

Generally:

/ 8�v8�v � 8�v / 8�w8�w � 8�w

Small-

signal

model

�� / �x 18�v � 18�v � �|8�w � D�xD��� / �x8�v � �| 18�w � 18�w � D�|D� � / �x8�v � �|8�w � D�xD� � D�|D�

/ 8�v8�v�x ≡ ��v�v�v / �x8�v� / �v � �w / �x8�v � �|8�w

1. I

2.

3.

4.

5.

Transient Response

35

�����

���

���M�6

������ �

"

��

�K �J

���

� / ��� �����

���8� ��

��� / ���M ���

�8

��(

<

Bn

p+

p-

� ��C

���� �M

��

�W ��0

Cut-off

"

<

0

active

�"

<

0

saturation

"

<

0

active

�"

<

0

saturation

1. I

2.

3.

4.

5.

Base Transient Time

36

"0

<active �� / �!�5 �∆<�0 FGHI

∆< A0C / !�5 ∆<A0, �C"�

� / !�"∆<A0C2/ !�5 2�!�"J�� / �A"J/25C8� / "J25

/ �8�

1. I

2.

3.

4.

5.

Turn ON

37

Turn-on: � / ��� / �D�D� / � � �8 → � � / �8 � �LO� �=⁄

I.C.: � 0 / 0 → � � / �8 1 � LO� �=⁄

→ �� � / � �8� / �88� 1 � LO� �=⁄ 0 � � � �K�� � / ��� / ���M

�� �� / ��� → �� / 8 ln 11 � ���� 8�8

1. I

2.

3.

4.

5.

Turn OFF

38

Turn-off: D�D� / ��� � �8 → � � / ���8 � �LO� �=⁄I.C.: � 0 ���� . / � ∞ ���� .x / �8

→ � � / �8 1 � � LO� �=⁄ � �→ ~�� � / ��� �W � � � ���� � / � �8� / �88� 1 � � LO� �=⁄ � � � � ��

��( / �� � �W → ��( / 8 ln 1 � ����� 8�8 � �

1. I

2.

3.

4.

5.

Non-Ideal BJT

39

1. Base width modulation (Early effect)

2. Punch-through

3. Avalanche Breakdown

4. Geometrical effects

5. Generation-Recombination in depletion regions

6. High-level injection

Deviations from Ideality:

1. I

2.

3.

4.

5.

Base Width Modulation

40

�� ≅ ��� / !�5<:" LP��= Q'⁄ � ↗⟶ " ↘⟶ �� ↗ ���

��� � 010��20��30��

�7 Early voltage

Saturation

�� / ��L�=� ��A1 � ���7 CActive:HW:

Show that 7 / !6"���

Emitter

np+

Base�" �

p-

Collector �“F” “R”

1. I

2.

3.

4.

5.

Punch Through

41

�����!� !�

Emitter

p+

Base�p-

Collector �“F” “R”

n

���

1. I

2.

3.

4.

5.

Avalanche Breakdown

42

���

��

���.��.���.

��.

���. / 1�K/� ��. n~4

1. I

2.

3.

4.

5.

Geometry Considerations

43

p-n-p Individual device n-p-n Integrated circuit BJT

� ��Current Crowding

1. I

2.

3.

4.

5.

G-R in Depl. Region , High-level injection

44

p-n-p Individual device

���

ln � , �)�() ∝ L�=���

∝ L�=�J��

∝ L�=�J��

High-level injection, Kirk Effect

��� In depletion region

�()

��

��� high injection

���

1. I

2.

3.

4.

5.

Small-Signal Model

45

Low Freq:B

E

C

������+

-��

E

C

������+

-�� ����� ��

��> / � �  �))�¡¡B

�� / ��� / ���¢/!�� / � �� / � . ��

�� / ��7�  / � :

1 � ��: �

��� / ���£1 � ��: � �; / KJ¤:8��� / ���¢/! 8� / ��. 8�

High Freq: