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Bipolar Junction Transistor Session 11: Solid State Physics 1

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Page 1: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

Bipolar Junction Transistor

Session 11: Solid State Physics

1

Page 2: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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Outline

� A� B

� C

� D

� E

� F� G

� H

� I

� J

2

Page 3: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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Introduction

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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

Page 4: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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BJT Types and Definitions

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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

�� ���

��� �

����� �� � ��

�� ���

�� ��

�����

Page 5: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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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…

Page 6: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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PNP BJT Operation (Qualitative)

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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)

Page 7: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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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

��� ������ ���

� ≡ ���

Page 8: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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BJT Circuit Configurations

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���

��� � 010��20��30��

Output Characteristics for Common-Emitter Configuration

CE: Common EmitterCB: Common Base CC: Common Collector

Page 9: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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BJT Modes of Operation

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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

Page 10: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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BJT Electrostatics

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

two independent pn junctions

������� �

Emitter

np+ p-

CollectorBase

pnp

Page 11: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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BJT Electrostatics

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

two independent pn junctions

������� �

Emitter

np+ p-

CollectorBase

pnp

Page 12: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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BJT Electrostatics

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������� �

Emitter

np+ p-

CollectorBasepnp

� �

!�!�

"

"

Page 13: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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BJT Electrostatics

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#

Emitter

np+ p-

CollectorBasepnp

� �""

$

Page 14: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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BJT Performance Parameters (PNP)

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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

Page 15: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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Collector Current (PNP)

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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 � &()/ �� � ���.

Page 16: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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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�:

≫ �

Page 17: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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“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

Page 18: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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Minority Carriers

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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

Page 19: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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Minority Carriers –Active

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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

Page 20: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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Minority Carriers –Saturation

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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

Page 21: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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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

Page 22: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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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

Page 23: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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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→

Page 24: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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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 >

Page 25: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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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� / �� � ��

Page 26: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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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

Page 27: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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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

Page 28: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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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-

��.

Page 29: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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Page 30: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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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; ⇈⇊

Page 31: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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ICEO and ICBO

31

np+ p-

��.

n

p+

p-

���.���. ≫ ��.

n

p+

p-

���.

���������

��

���. / ��� � ��� / ��. � �()��.

Page 32: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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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⁄

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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

&����

�� ��� ��

Page 34: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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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

Page 35: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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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

Page 36: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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Base Transient Time

36

"0

<active �� / �!�5 �∆<�0 FGHI

∆< A0C / !�5 ∆<A0, �C"�

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

/ �8�

Page 37: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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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

Page 38: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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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 � �

Page 39: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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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:

Page 40: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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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”

Page 41: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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Punch Through

41

�����!� !�

Emitter

p+

Base�p-

Collector �“F” “R”

n

���

Page 42: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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Avalanche Breakdown

42

���

��

���.��.���.

��.

���. / 1�K/� ��. n~4

Page 43: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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Geometry Considerations

43

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

� ��Current Crowding

Page 44: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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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

���

Page 45: Session 11: Solid State Physics Bipolar Junction Transistoree.sharif.edu/~sarvari/25772/PSSD010.pdf · Bipolar Junction Transistor ... minority-carrier diffusion equation ... Ebers-Moll

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Small-Signal Model

45

Low Freq:B

E

C

������+

-��

E

C

������+

-�� ����� ��

��> / � �  �))�¡¡B

�� / ��� / ���¢/!�� / � �� / � . ��

�� / ��7�  / � :

1 � ��: �

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

High Freq: