The first Transistor

[ 半導體元件概論 -2009] 

3. 雙極性接面電晶體 

(Bipolar Junction Transistor, BJT) 

王水進教授 

成大電機系微電子研究所 

1 

The first Transistor 

[S. M. Sze, Semiconductor Device Physics and Technology, John Wiley, 1985] 

Emitter 

Collector 

Base 

2 

1

The discovery of the point 

contact transistor in 1947 

This work resulted in their 

receiving the Nobel Prize 

for Physics in 1956. 

雙極性電晶體發明人 

[http://www.att.com/technology/history/chronolog/47transistor.html] 

3 

典型 BJT 封裝 

[Earl D. Gates, Introduction to electronics, 4/e, Delmar, Thomson Learning Inc., 2001 ] 

4 

2

Perspective view of an oxide-isolated BJT 

[http://ceiba.cc.ntu.edu.tw/542U0130/u0130/electro/form6.htm] 

5 

Basic structures of BJTs 

[D. A. Neamen, Semiconductor Physics and Devices, IRWIN, 1997] 

[Encyclopedia Americana, http://go.grolier.com:80/] 

Conventional IC npn BJT 

An oxide-isolated npn BJT 

6 

3

NPN Bipolar Transistor 

Planar junction (Bipolar) transistor 

Emitter 

Base 

Collector 

Al•Cu•Si 

SiO 2 

n p n 

p + 

+ 

+ n-epi 

Electron flow 

n + buried layer 

P-substrate 

p + 

7 

Cross sections of BJTs 

[R. F. Robert, Semiconductor Device Fundamentals, Addison Wesely, 1996] 

A typical discrete, 

double-diffused pnp BJT 

An IC npn BJT 

8 

4

典型雙極性接面電晶體結構 

[ 王水進 , 電子學 - 基礎篇 , 全華科技圖書 ,1998] 

B 

E 

B 

垂直型 

( 縱向型 ) 

n + 

p 

n 

n + 

E 

C 

B 

C 

10 20 

射極 

n + 

基極 

p 

集極 

n n + 

水平型 

( 橫向型 ) 

p + 

n+ 

p n + 

n 

p + 

n + − 掩埋層 

SiO 2 

-3 

摻雜濃度 (cm ) 

10 18 

10 16 

p− 

Si基板 

雜質分佈曲線 

深度 

9 

Bipolar junction transistor 

[From Wikipedia, the free encyclopedia] 

[http://en.wikipedia.org/wiki/Bipolar_junction_transistor] 

A bipolar (junction) transistor (BJT) is a type of transistor. It is a three-terminal 

device constructed of doped semiconductor material and may be used in 

amplifying or switching applications. 

Although a small part of the transistor current is due to the flow of majority 

carriers, most of the transistor current is due to the flow of minority carriers and 

so BJTs are classified as minority-carrier devices. 

10 

5

The bipolar Junction Transistors 

[http://dspace.mit.edu/bitstream/handle/1721.1/36373/6-012Spring-2003/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6- 

012Microelectronic-Devices-and-CircuitsSpring2003/DD39CE25-C7AA-4503-999C-5E529728AE6A/0/lecture17.pdf] 

11 

Concept of 

Transistor Action 

6

雙極性電晶體之基本操作 : 

典型 pn 接面於偏壓下多數與少數載子之電通量 


順偏 

反偏 

I 

n + 

p 

I o 

p 

n 

I o 

I 

F pp 

>> 

F nn 

F np 

F pn 

多數載子電通量 

少數載子電通量 

13 


不同基極寬度下由射極注入基極電子流之流動方向 

順偏反偏 

n + 

p 

n 


I E 

I C 

IE= IC+ IB>> 

IB 

0 W 

I B 

W

Current components in a BJT 

[From Wikipedia, the free encyclopedia] 

[http://en.wikipedia.org/wiki/Bipolar_junction_transistor] 

15 

Carrier transport in a BJT 

[http://dspace.mit.edu/bitstream/handle/1721.1/36373/6-012Spring-2003/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6-012Microelectronic-Devices-and- 

CircuitsSpring2003/DD39CE25-C7AA-4503-999C-5E529728AE6A/0/lecture17.pdf] 

16 

8

Typical output characteristics of a BJT 

[Kwok K. Ng, Complete Guide to Semiconductor Devices, 2/e, McGraw-Hill, 2002] 

共基 (CB) 組態 

共射 (CE) 組態 

17 

Transistor (= Transfer Resistor) 

 

v I 

i C 

V CC 

RC 

i B + 

v CE 

- 

v O 

Load line 

V 

CC 

= i 

Q 1 : low resistance 

Q 2 : high resistance 

C 

R 

C 

+ v 

CE 

18 

9

Switching operation of BJT 

V CC 

i C RC 

i B v O 

v I 

5V 

0 

V CC 

0 

v I 

v O 

t 

t 

V 

R 

CC 

C 

C 

¹¡¦X 

B 

A 

i B 

I off 

i C 

V CC 

v CE 

0 

19 

[http://www.interfacebus.com/FETs.html#a] 

Operation Theory of 

BJTs 

10


由射極注入基極載子流之流動方向 


n p n 

p n p 

I E 

I C 

I E 

I C 

I B 

I B 

- V BE 

+ -V CB 

+ 

+ V EB 

- +V BC 

- 

21 

Definition of BJT operation regions 

[S. M. Sze, Modern Semiconductor Device Physics, John Wiley, 1998] 

22 

11

Minority carrier distribution in an npn BJT 


23 

Carrier profiles in forward-active regime 

[http://dspace.mit.edu/bitstream/handle/1721.1/36373/6-012Spring-2003/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6-012Microelectronic-Devices-and- 


24 

12

Ideal pn junction current 

J 

J 

p 

n 

J p 

(x), J n 

(x) 

-x p 

0 

x n 

總電流 

J p ( x n ) 

J n (x) 

Jn( −xp) 

J p (x) 

Key concept 

= qA 

= qA 

Dp 

Lp 

Dn 

Ln 

p 

n 

no 

po 

⋅e 

⋅e 

VA 

/ VT 

VA 

/ VT 

⎫ 

⎪ 

⎬ 

⎪ 

⎭ 

⇒ 

J 

J 

p 

n 

N 

∝ 

N 

A 

D 

x 

I = AJ = A[ 

J 

Dn 

= qA[( 

n 

L 

I 

= I 

o 

o 

( e 

= qA[ 

= qA[( 

∝ e 

n 

VA 

V T 

− 

−1) 

D 

L 

Eg 

kT 

p 

po 

n 

n 

n 

D 

L 

( xn) 

+ J 

Dp 

+ p 

L 

po 

n 

nND 

p 

+ 

+ 

n 

( −x 

no 

Dp 

Lp 

Dp 

L N 

p 

)( e 

A 

p 

p 

)] 

V A 

V T 

−1)] 

no 

] 

)] n ] 

2 

i 

25 

Derivation of I-V equations of BJTs 

x 

 

x n 

Eo 

p 

x x LE 

P n P 

pn( x) 

nx ( ) = n −Δnx ( ) e 

Co 

0 ≤ x ≤W B 

n 

−( x−xn)/ 

LC 

nE ( x) 

n Eo 

− x p 

p Bo 

0 

W B 

nC ( x ) 

− x n 

p Co 

−W 

/ L 

B B 

B 

ΔpW ( B ) − Δp( 0) 

e 

x/ 

L ΔpW ( B ) − Δp( 0) 

e 

B 

px ( ) = pBo[( 

) e − ( 

2 sinh( W / L ) 

2 sinh( W / L ) 

B 

B 

B 

W / LB 

B 

− x/ 

L 

B 

) e ] 

27 

13

Derivation of I-V equations of BJTs 

I E = AE 

( J pE + J nE ) = AE 

[ J p ( x = 0) + J n ( x = − x p )] 

∂ p ( x ) 

∂ n( 

x) 

= AE 

[( − q D B 

x = 0 ) + ( − q D E 

x = − x )] 

p 

∂ x 

∂ x 

q D B p Bo W 

= A 

coth ( B )[( V EB / VT 

E 

e − 1) 

L B L B 

1 

− ( −V 

BC / V 

q D E n EO 

e 

T − 1)] + A 

( V EB / VT 

E e − 1) 

W B 

cosh ( ) 

L 

L 

E 

B 

I C = AC 

( J pC + JnC 

) = AC 

[ J p( 

x = WB 

) + Jn( 

x = xn)] 

∂ px ( ) 

∂ nx ( ) 

= ( − qDB x= W ) + ( −qDC x= 

x ) 

∂x 

B 

∂x 

n 

− 

= A qD B p Bo 1 V W 

EB VT B VBC VT 

C 

[( e 

−1) −coth( )( e 

W 

L 

B 

B sinh( ) L 

L 

B 

B 

−1)] 

− 

−A C n Co VBC 

/ VT 

C ( e 

LC 

−1) 

28 


operating in the active mode 

[A. S. Sedra and K. C. Smith, Microelectronic Circuits, Oxford Univ. Press, 1998] 

Emitter 

(n) 

E-B 

depletion region 

Base 

(p) 

B-C 

depletion region 

Collector 

(n) 

n p (0) 

p n (0) 

p no 

n (0) = n 

p 

p (0) = p 

n 

e 

vBE 

/ VT 

po 

vBE 

VT 

noe 

/ 

0 

I n 

n p (x) 

(ideal) 

n p (x) 

W 

(with recombination) 

I 

n 

dnp( 

x) 

= AE 

qDn 

dx 

np 

( o) 

= AE 

qDn 

( − ) 

W 

x 

29 

14


operating in the active mode 

[S. M. Sze, Semiconductor Devices, Physics and Technology, John Wiley, 1985] 

30 



Saturation 

Cut-off 

31 

15

熱平衡狀態下 BJT 之能帶圖 


32 

順向作用區工作電晶體之能帶圖 

結構示意圖 

+ − 

E 

+ 

X E 

p 

X B 

n 

X C 

p 

I C 

− 

C 

能帶圖 

I E 

V EB 

電荷分佈圖 

V EC 

I B 

− + 

B 

V BC 

qV 

E CB qV c CE 

qV EB 

E v 

qN ( D − NA) 

N B 

x n 

− x p 

0 W B 

x 

N C 

N E 

33 

16

電晶體之能帶圖 

p 

n 

p 

n 

p 

n 

E c 

E c 

E v 

E v 

熱平衡 

狀態 

E c 

E v 

E F 

E c 

E v 

E v 

qV Do 

E F 

qV Do 

qV D 

順向操作 

狀態 

E c 

E v 

E c 

qV CB qV CE qV qVCB 

EB 

qV CE 

qV EB 

qV D 

34 

E 

I B 

pnp 電晶體之電流成份 

p n p 

I E 

I Ep 

( Ep − ICp) 

I Cp I C 

+ 

I CBOp 

I En 

I CBOn 

- 

C 

I 

I 

Ep 

γ ≡ ≈1− 

E 

σ BW 

σ W 

E 

V EB 

Emitter efficiency 

α T 

I 

I 

Cp 

≡ ≈1 

− 

Ep 

W 

B 

E 

2 

B 

2 

p 

2 L 

- 

B 

Base transport efficiency 

CB SC current gain 

I 

I 

C 

α( ≡ = γα ) 

E 

T 

+ 

V BC 

IE = IEp + I En 

I = I + ( I − I ) − I 

B En Ep Cp CBO 

I E = I C + I B 

I ( = I + I ) 

CBO CBOp CBOn 

I = αI + I 

C E CBO 

I = I + I = γ α I + I 

C Cp CBO T E CBO 

35 

17

Diffusion currents flowing in 

a pnp BJT under active mode biasing 


CB dc current gain α dc 

I Cp = αT 

I Ep = γ αT 

I 

Emitter efficiency Base transport factor 

E 

I 

I 

γ = EP 

ICP 

C = α dcIE 

+ ICB0 

= ICp 

+ ICn 

α T = 

IE 

I 

= γ α I + I 

EP 

T 

E 

Cn 

⇒ 

α 

dc 

= γ α , 

T 

I 

CB0 

= I 

Cn 

I 

C 

= β 

= α 

CB dc current gain β dc 

dc 

dc 

IB 

+ I 

( I + I 

C 

CB0 

B 

= α 

) + I 

I 

dc E 

CB0 

+ I 

CB0 

α dc 1 

IC 

= IB 

+ I 

1−α 

dc 1−α 

dc 

= β dcIB 

+ (1 + β dc) 

I 

α dc 

β dc 

−α 

dc 

CB0 

CB0 

36 

= 1 

37 

Current-Voltage Characteristics of BJTs 

(Gummel plot) 

[B. G. Streetman and S. Banerjee, Solid State Electronic Devices, Prentice Hall, 2000] 

High level 

injection 

Base resistance 

ideal 

ideal 

V EB 

log I C 

ideal 

37 

18

Gummel plot and dc current gain 


Ideal 

High-level injection, 

current crowding, 

and/or series resistance 

β dc 

V BC = 5V 

Ideal 

V EB 

I C 

(A) 

Data derived from a 2N2605 pnp BJT 

38 

Gummel plot: semilog plot of IC and IB vs. VBE 

[http://dspace.mit.edu/bitstream/handle/1721.1/36373/6-012Spring-2003/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6- 

012Microelectronic-Devices-and-CircuitsSpring2003/DD39CE25-C7AA-4503-999C-5E529728AE6A/0/lecture17.pdf] 

39 

19

Gummel plot of BJT (VCE = 3 V ) 

[http://dspace.mit.edu/bitstream/handle/1721.1/36373/6-012Spring-2003/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6-012Microelectronic-Devices-and- 40 


Current-Voltage 

Characteristics of BJTs 

41 

20

BJT 應用之三種組態 


+ 

I B 

V 

+ 

CE 

V BE 

− 

I E 

I C 

− 

V BE 

+ I B 

− 

V CB 

V 

− 

CB 

I 

+ 

C 

I E I C 

− 

+ 

I B 

I E 

− 

V CE 

+ 



共集 (CC) 組 

42 

共基 (CB) 組態電晶體特性 

I E 

(mA) 

10 

8 

6 

VCB = 15V 

VCB = 10V 

VCB = 5V 

4 

2 

0 

0.6 0.7 0.8 0.9 

V BE 

(Volts) 

I C 

(mA) 

10 

8 

6 

4 

2 

IE = 10 mA 

IE = 8 mA 

IE = 6 mA 

IE = 4 mA 

IE = 2 mA 

I CBO 

IE = 0 mA 

0 1 2 3 4 5 6 

VBE ( Volts) 

I E I C 

I B I B 

I E I C 

− 

V BE 

+ 

+ 

V CB 

− 

+ 

V EB 

− 

− 

V BC 

+ 

43 

21

共射 (CE) 組態電晶體特性 

3 

20 

18 

16 

I B =100 uA 

I B 

(μA) 

2 

1 

VCE = 5V 

VCE = 15V 

I C (mA) 

14 

12 

10 

8 

6 

80 uA 

60 uA 

40 uA 

4 

20 uA 

0 04 . 06 . 08 . 10 . 12 . 14 . 

VBE ( Volts) 

2 

0 uA 

0 

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 

V CB (V) 

I C 

I C 

I B 

+ 

+ 

V CE 

V BE − 

I 

− 

E 

− 

V EB 

+ 

I B 

I E 

− 

V EC 

+ 

44 

Typical output characteristics of a BJT 

[Kwok K. Ng, Complete Guide to Semiconductor Devices, 2/e, McGraw-Hill, 2002] 



45 

22

共集 (CC) 組態電晶體特性 

I B (mA) 

20 

18 

15 

13 

V CB = 5 V 

V CB = 10 V 

V CB = 15 V 

10 

8 

5 

3 

0 

0 2 4 6 8 10 12 14 16 

V CB (V) 

I E (mA) 

20 

18 

16 

14 

12 

10 

8 

6 

4 

2 

IB = 100 μ A 

80 μA 

60 μA 

40 μA 

20 μA 

0 μA 

0 

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 

V CE (V) 

I E 

I E 

− 

V BC 

+ 

I B 

I C 

− 

V CE 

+ 

+ 

I B 

V BC I − 

+ 

− 

C 

V EC 

46 

Figure-of-Merit (FOM) for BJT performance 


Current gain cutoff frequency, f T 

The frequency at which the short-circuit current gain (h fe 

, or β) drop to 

unity. 

A key estimator of transistor high-speed performance 

1 

wc 

( kT / q) 

= τ b + τ e' 

+ + ( RE 

+ RC 

) CBC 

+ ( CBE 

+ CBC 

) 

2π fT 

2vs 

IC 

Maximum frequency of oscillation, f max 

The frequency at which the maximum available power gain (MAG) of 

the transistor drops to unity. 

F max 

is different from (and typically larger than) f T 

, because in 

addition to current gain, f max 

takes into account the possibility of 

voltage gain. 

fmax 2 1 Re( Zin) 

2 

G p = ( ) = [ ] h fe 

f 4 Re( Zout 

) 

T 1/ 2 

max ( ) 

8π RBCBC 

f = 

f 

Figure of Merit: 效益指數、評量指標 

47 

23

Figure-of-Merit for BJT performance 


48 

Non-ideal effects of BJTs 

49 

24

BJT 之穿透崩潰 (punch-through breakdown) 

W B 

E 

N + P N 

C 

punch-through 

breakdown voltage 

Depletion 

region 

B 

V 

2 

PT B B s 

( = qN W / 2ε ) 

W B 

V B 

E 

N + P N 

B 

Depletion 

region 

C 

ΔV B 

發生穿透崩潰時 

V + V 

bi CB 

E c 

E c 

50 

電晶體與兩端間之崩潰曲線 ( 第三端開路 ) 

I 

1 

M = 

V 

1 − ( ) 

I CEO 

BV CBO 

m 

I 

CEO 

BV CEO 

I CBO 

BV CBO 

1/ m 

β 

I CBO 

= 

1−α 

M 

V 

BV 

CEO 

= BV 

BV 

≈ 

CBO 

CBO 

(1− 

α) 

I B = 0 

I CEO 

I CBO 

I E = 0 

1/ m 

51 

25

The avalanche breakdown in a transistor 


52 

Carrier multiplication and feedback mechanism 


0: initial hole injection 

1: injected hole entering the CB 

depletion junction 

2: e-h pair generation by impact ionization 

3: generated electrons being swept 

into the vase 

4: excess base electrons injected 

into the emitter 

5: hole injected from the emitter 

into the base in response to the 

step 4 electron injection 

53 

26

Non-ideal I-V characteristics of BJTs 


Non Early effect 

no carrier multiplication 

With Early effect and 

carrier multiplication 

With Early effect 

no carrier multiplication 

54 

The Early effect 


55 

27

Dependence of i C on the collector voltage – 

the Early effect 

[A. S. Sedra and K. C. Smith, Microelectronic Circuit, Oxfor Univ. Press, 1998] 

i 

C 

v 

/ CE 

= I v V 

Se 

BE T (1 + ) Output resistance 

V 

A 

⎡ ∂i 

ro 

≡ ⎢ 

⎣∂v 

C 

CE 

vBE 

=const. 

⎤ 

⎥ 

⎦ 

−1 

56 

Geometrical effect- 

current crowding 

Emitter area ≠ collector area 

Bulk and contact resistance 

(using thin epilayer or heavily doped buried layer) 

57 

28

Current crowding 

58 

Cross section of a BJT under active bias 

C-B 

space-charge 

layer 

Collector region 

Lines of flow of 

majority carriers 

The base current is supplied form two side base contact and flows 

toward the center of the emitter causing the BE voltage drop to vary 

with position. 

62 

29


Extrinsic base resistance 

ρBX 

L ρBX 

d 

R1 

= = 

A ( x + x ) W 

E 

B 

Intrinsic base resistance 

R 

2 

ρBIh 

= 

3x 

W 

B 


R = r 

b 

= RC 

+ R1 

+ R2 

x 

63 

Effect of Base Resistance 


64 

30

An interdigitated geometry 

to release the effects of emitter current crowding 


top view of 

implanted region 

65 

Geometry design of power BJTs 

66 

31

Transistor collector resistance R CS 

In active region 

the collector junction is reveres biased 

and hence represents a rather high 

impedance. The collector voltage 

drop I C 

R CS 

is normally small 

compared to the collector junction 

resistance and can be neglected. 

In saturation region 

The collector junction is forward biased, the collector bulk voltage drop 

generally even exceeds the potential drop across the junction. 

The effect is most pronounced at low CE voltages where the BJT 

is in saturation and hence is collecting minority carrier inefficiently 

(the collector is back injection to the emitter). 

67 

Emitter-collector shorts caused by diffusion pipes or spikes 

through the base along the dislocations 

Diffusion pipes 

Diffusion spikes 

Dislocations: 

oxidation induced stacking faults, epitaxial-growth-induced 

slip dislocations, and other process-induced defects 

68 

32

The first Transistor

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