Post on 26-Mar-2020
Lundstrom ECE-606 S13
Notes for ECE-606: Spring 2013
Bipolar Junction
Transistors (BJTs)
Professor Mark Lundstrom Electrical and Computer Engineering
Purdue University, West Lafayette, IN USA lundstro@purdue.edu
1 3/21/13
2
Reversve biased PN junction
Fig. 6.9, Semiconductor Device Fundamentals, R.F. Pierret
Current is small
3
PN junction in reverse bias
Lundstrom ECE-606 S13
Fp
EC
Fn
EV
hf > EG
Large currents can flow when there are excess minority carriers on the P-side (or N-side).
4
excess carriers another way
Lundstrom ECE-606 S13
FpEC
FnEV
Fn VBE > 0
p0P ≈ NA
Fp
E
C B
VCB > 0
25
generic transistor
Lundstrom ECE-606 S13
I1
3
V32
ΔI1 = gmΔV32
gm =∂I1∂V32 V12
1
I2
6
BJT
Lundstrom ECE-606 S13
IC
VBE
ΔIC = gmΔVBE
gm = ∂IC∂VBE VCE
IE
E
C
B VCE
VCB =VCE −VBE
7
invention of the transistor
1926
C.T. Sah, “Evolution of the Field-Effect Transistor – From Conception to VLSI,” Proc. IEEE, 76, 1280, 1988
8
“discovery” of the bipolar transistor
0http://www.porticus.org/bell/images/transistor1.jpg
9
inventors of the bipolar transistor
http://en.wikipedia.org/wiki/File:Bardeen_Shockley_Brattain_1948.JPG
NPN bipolar transistor
10
IC
IB VCE
VBE
VCB
IE
IB + IC = IE
VBE +VCB = VCE
KCL:
KVL:
NPN bipolar transistor
11
IC
IB VCE
VBE
VCB
IE n+ emitter
p base
n collector
n+
C
B
E
transistor structures
12
n+ emitter
p base
n collector
n+
p base n-collector
n+
n+
double
diffused
BJT
common base (active region)
13
IC
IB VCE
VBE
VCB
IE
IC
VCBVEB IB
IE
BE: FB BC: RB
VEB < 0VCB > 0
common emitter (active region)
14
IC
IB VCE
VBE
VCB
IE
BE: FB BC: RB
VBE > 0VCB = VCE −VBE > 0
IC
IB VCE
IEVBE
BJT operation: active region
15 15
n+ emitter
p base
n collector
n+
FB RB
1) energy band diagram
BJT operation: active region currents
16 16
n+ emitter
p base
n collector
n+
FB RB IE IC
IB
IEn
IEpIE = IEn + IEp
ICn
ICp
ICn ≈ IEn >> ICp
IC ≈ IEn
IB ≈ IEp
(neglect base recombination)
2) currents
BJT operation: active region
17 17
n+ emitter
p base
n collector
n+
FB RB IE ICIEn
IEpIE = IEn + IEp
IEn
IC ≈ IEn
IB = IEp
3) Boundary conditions at the beginning and end of the base.
BJT operation: active region
18
18 xp
x
Δn x( )
WB+xp
n+ emitter
p base
n collector
n+
FB RB IE ICIEn
IEpIE = IEn + IEp
IEn
IC ≈ IEn
IB = IEp
Δn(0) = ni2
NAB
⎛⎝⎜
⎞⎠⎟eqVBE kBT −1( )
Δn(WB + xp ) =ni2
NAB
⎛⎝⎜
⎞⎠⎟eqVBC kBT −1( )
base diffusion current
19
0 x
Δn x( ) Δn 0( )
WB
Δn WB( ) ≈ 0Δn(0) = ni
2
NAB
⎛⎝⎜
⎞⎠⎟eqVBE kBT −1( )
IEn = qAEni2
NAB
⎛⎝⎜
⎞⎠⎟Dn
WB
eqVBE /kBT −1( )
IEn
IEn = −qAEDndn(x)dx
= qAEDnΔn(0)WB
BJT operation: beta
20 20
n+ emitter
p base
n collector
n+
FB RB IE ICIEn
IEpIE = IEn + IEp
ICn
IC ≈ IEn
IB = IEp
IEn = qAEni2
NAB
⎛⎝⎜
⎞⎠⎟Dn
WB
eqVBE /kBT −1( ) ≈ IC
IEp = qAEni2
NDE
⎛⎝⎜
⎞⎠⎟Dp
WE
eqVBE /kBT −1( ) ≈ IBβ =
ICIB
=NDE
NAE
Dn
Dp
WE
WB
BJT operation: transconductance
21
21
n+ emitter
p base
n collector
n+
FB RB IE ICIEn
IEpIE = IEn + IEp
IEn
IC ≈ IEn
IB = IEp
IC = qAEni2
NAB
⎛⎝⎜
⎞⎠⎟Dn
WB
eqVBE /kBT −1( )= IC0 e
qVBE /kBT −1( )
gm =∂IC∂VBE
=IC
kBT q( )
gm =ID
VGS −VT( )
BJT operation: gamma
22 22
n+ emitter
p base
n collector
n+
FB RB IE ICIEn
IEpIE = IEn + IEp
IEn
IC ≈ IEn
IB = IEp
IEn = qAEni2
NAB
⎛⎝⎜
⎞⎠⎟Dn
WB
eqVBE /kBT −1( ) ≈ IC
IEp = qAEni2
NDE
⎛⎝⎜
⎞⎠⎟Dp
WE
eqVBE /kBT −1( ) ≈ IBγ =
IEnIEn + IEp
< 1
BJT operation: base transport factor
23 23
n+ emitter
p base
n collector
n+
FB RB IE ICIEn
IEpIE = IEn + IEp
ICn
IC ≈ IEn
IB = IEp
IEn = qAEni2
NAB
⎛⎝⎜
⎞⎠⎟Dn
WB
eqVBE /kBT −1( )
IEp = qAEni2
NDE
⎛⎝⎜
⎞⎠⎟Dp
WE
eqVBE /kBT −1( ) ≈ IB
ICn = αT IEn ≈ IC
BJT operation: IE and IC
24 24
n+ emitter
p base
n collector
n+
FB RB IE ICIEn
IEpIE = IEn + IEp
ICn
IC ≈ IEn
IB = IEp
ICn = αT IEn = IC
γ =IEn
IEn + IEp=IEnIE
IC = αT IEn = αTγ IE = αdcIE
IB = IE − IC = IC β
IC = αdcIE
αdc = αTγ
β =αdc
1−αdc
common emitter (active region)
25
IC
IB VCE
VBE
VCB
IE
IC = βIB
IB VCE >VBE
IE = β +1( ) IB
VBE > 0
IV characteristics
Gummel plot
26
log J( )
VBE
JC = JC0 eqVBE /kBT −1( )
JB = JB0 eqVBE /nkBT −1( )
NPN bipolar transistor
27
BE: FB BC: RB
VBE > 0VCB = VCE −VBE > 0
IC
IB VCE
IEVBE
Pierret, Fig. 10.4
active saturation
cut-off inverted active
BJT operation: active region
28
28
xp x
Δn x( )
WB+xp
Δn(0) = ni2
NAB
⎛⎝⎜
⎞⎠⎟eqVBE kBT −1( )
Δn(WB + xp ) =ni2
NAB
⎛⎝⎜
⎞⎠⎟eqVBC kBT −1( )
Δn(WB + xp ) ≈ 0Pierret, Fig. 10.4
active saturation
cut-off inverted active
VBE > 0
VCB > 0
BJT operation: saturation region
29
29
xp x
Δn x( )
WB+xp
Δn(0) = ni2
NAB
⎛⎝⎜
⎞⎠⎟eqVBE kBT −1( )
Δn(WB + xp ) =ni2
NAB
⎛⎝⎜
⎞⎠⎟eqVBC kBT −1( )
Δn(WB + xp ) >> 0Pierret, Fig. 10.4
active saturation
cut-off inverted active
VBE > 0VCB < 0
BJT operation: cut-off region
30
30
xp x
Δn x( )
WB+xp
Δn(0) = ni2
NAB
⎛⎝⎜
⎞⎠⎟eqVBE kBT −1( )
Δn(WB + xp ) =ni2
NAB
⎛⎝⎜
⎞⎠⎟eqVBC kBT −1( )
Pierret, Fig. 10.4
active saturation
cut-off inverted active
VBE ≤ 0
VCB ≥ 0
BJT operation: inverted active region
31
31
xp x
Δn x( )
WB+xp
Δn(0) = ni2
NAB
⎛⎝⎜
⎞⎠⎟eqVBE kBT −1( ) ≈ 0
Δn(WB + xp ) =ni2
NAB
⎛⎝⎜
⎞⎠⎟eqVBC kBT −1( )
Δn(WB + xp ) >> 0 Pierret, Fig. 10.4
active saturation
cut-off inverted active
VBE ≤ 0VCB < 0
NPN bipolar transistor (active region)
32
1) Base recombination (base transport factor)
2) Speed (frequency response)
3) Base width modulation (Early effect)
4) Typical doping profiles
5) Kirk effect
base recombination
33
0 x
Δn x( )
Δn 0( )
WB
Δn WB( ) ≈ 0
IEn
quasi-neutral base
ICn ≈ IEn
IEn − ICn ≈ AEqΔn 0( )WB
2τ n
IEn −αT IEn ≈ AEqΔn 0( )WB
2τ n
1−αT ≈AE
qΔn 0( )WB
2τ nIEn
⎛
⎝
⎜⎜⎜⎜
⎞
⎠
⎟⎟⎟⎟
IEn = qAEDnΔn 0( )WB
αT ≈ 1− 12
WB
Ln
⎛⎝⎜
⎞⎠⎟
2
speed (base transit time)
34
0 x
Δn x( )
Δn 0( )
WB
Δn WB( ) ≈ 0
IEn
quasi-neutral base
ICn ≈ IEn
IC = qAEDnΔn 0( )WB
IC =QB
tt
QB =qΔn 0( )WB
2
tt =WB
2
2Dn
fT =12πtt
effects of saturation on speed
35 Pierret, Fig. 12.7
Early effect (base width modulation)
36
BE: FB BC: RB
VBE > 0VCB = VCE −VBE > 0
IC
IB VCE
IEVBE
Pierret, Fig. 10.4
active saturation
cut-off inverted active
Why is there an output conductance (resistance)?
Early effect (base width modulation)
37
n+ emitter
p base
n collector
n+
FB RB IE ICIEn ICn
IC ≈ IEn
Width of the quasi-neutral base is what matters. Width of the CB depletion region depends on base doping, collector doping, and revers bias across the C-B junction.
IC ∝ DnΔn 0( )WB
typical doping profiles
38 38
n+ emitter
p base
n collector
n+
FB RB IEn
IEp
IEn ∝ni2
NAB
IEp ∝ni2
NDE
γ =IEn
IEp + IEn≈
1
1+ NAB
NDE
⎛⎝⎜
⎞⎠⎟
Emitter must be doped more heavily than the base.
HBT
39 39
n+ emitter
p base
n collector
n+
FB RB
EGE EGB EGC
IEn
IEp
IEn ∝niB2
NAB
IEp ∝niE2
NDE
γ =IEn
IEp + IEn≈
1
1+ niE2
niB2NAB
NDE
⎛⎝⎜
⎞⎠⎟
Freedom to dope the base heavily
collector doping
40 40
n+ emitter
p base
n coll
n+
FB RB IEn
IEp
ρ = qNDJC = q Dn
WB
Δn 0( )
JC = qnυsatn ≈ ND
“base push out” Kirk effect
common base (active region)
41
IC
IB VCE
VBE
VCB
IE
IC = αdcIE
VCB > 0VEB < 0
IE
IB = IC β
IV characteristics
common base (active region)
42
IC
VCBVEB IB
IE
BE: FB BC: RB
VEB < 0VCB > 0
Pierret, Fig. 10.4
active
cut-off
saturation