Notes for ECE-606: Spring 2013 Bipolar Junction Transistors (BJTs) Professor Mark Lundstrom Electrical and Computer Engineering Purdue University, West Lafayette, IN USA [email protected]1 3/21/13 2 Reversve biased PN junction Fig. 6.9, Semiconductor Device Fundamentals, R.F. Pierret Current is small
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Bipolar Junction Transistors (BJTs)BJTs.pdf · Fig. 6.9, Semiconductor Device Fundamentals, R.F. Pierret Current is small . 3 PN junction in reverse bias Lundstrom ECE-606 S13 F p
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Lundstrom ECE-606 S13
Notes for ECE-606: Spring 2013
Bipolar Junction
Transistors (BJTs)
Professor Mark Lundstrom Electrical and Computer Engineering
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.