Bipolar Junction Transistors (BJTs) - nanoHUBBJTs.pdf · Bipolar Junction Transistors (BJTs)...
Transcript of Bipolar Junction Transistors (BJTs) - nanoHUBBJTs.pdf · Bipolar Junction Transistors (BJTs)...
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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
Purdue University, West Lafayette, IN USA [email protected]
1 3/21/13
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Reversve biased PN junction
Fig. 6.9, Semiconductor Device Fundamentals, R.F. Pierret
Current is small
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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).
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excess carriers another way
Lundstrom ECE-606 S13
FpEC
FnEV
Fn VBE > 0
p0P ≈ NA
Fp
E
C B
VCB > 0
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generic transistor
Lundstrom ECE-606 S13
I1
3
V32
ΔI1 = gmΔV32
gm =∂I1∂V32 V12
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I2
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BJT
Lundstrom ECE-606 S13
IC
VBE
ΔIC = gmΔVBE
gm =∂IC∂VBE VCE
IE
E
C
B VCE
VCB =VCE −VBE
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invention of the transistor
1926
C.T. Sah, “Evolution of the Field-Effect Transistor – From Conception to VLSI,” Proc. IEEE, 76, 1280, 1988
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“discovery” of the bipolar transistor
0http://www.porticus.org/bell/images/transistor1.jpg
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inventors of the bipolar transistor
http://en.wikipedia.org/wiki/File:Bardeen_Shockley_Brattain_1948.JPG
NPN bipolar transistor
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IC
IB VCE
VBE
VCB
IE
IB + IC = IE
VBE +VCB = VCE
KCL:
KVL:
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NPN bipolar transistor
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IC
IB VCE
VBE
VCB
IE n+ emitter
p base
n collector
n+
C
B
E
transistor structures
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n+ emitter
p base
n collector
n+
p base n-collector
n+
n+
double
diffused
BJT
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common base (active region)
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IC
IB VCE
VBE
VCB
IE
IC
VCBVEB IB
IE
BE: FB BC: RB
VEB < 0VCB > 0
common emitter (active region)
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IC
IB VCE
VBE
VCB
IE
BE: FB BC: RB
VBE > 0VCB = VCE −VBE > 0
IC
IB VCE
IEVBE
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BJT operation: active region
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n+ emitter
p base
n collector
n+
FB RB
1) energy band diagram
BJT operation: active region currents
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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
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BJT operation: active region
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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
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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( )
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base diffusion current
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0 x
Δn x( ) Δn 0( )
WB
Δn WB( ) ≈ 0Δn(0) = ni
2
NAB
⎛⎝⎜
⎞⎠⎟eqVBE kBT −1( )
IEn = qAEni2
NAB
⎛⎝⎜
⎞⎠⎟DnWB
eqVBE /kBT −1( )
IEn
IEn = −qAEDndn(x)dx
= qAEDnΔn(0)WB
BJT operation: beta
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n+ emitter
p base
n collector
n+
FB RB IE ICIEn
IEpIE = IEn + IEp
ICn
IC ≈ IEn
IB = IEp
IEn = qAEni2
NAB
⎛⎝⎜
⎞⎠⎟DnWB
eqVBE /kBT −1( ) ≈ IC
IEp = qAEni2
NDE
⎛⎝⎜
⎞⎠⎟DpWE
eqVBE /kBT −1( ) ≈ IBβ = IC
IB=NDENAE
DnDp
WEWB
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BJT operation: transconductance
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n+ emitter
p base
n collector
n+
FB RB IE ICIEn
IEpIE = IEn + IEp
IEn
IC ≈ IEn
IB = IEp
IC = qAEni2
NAB
⎛⎝⎜
⎞⎠⎟DnWB
eqVBE /kBT −1( )= IC0 e
qVBE /kBT −1( )
gm =∂IC∂VBE
=IC
kBT q( )
gm =ID
VGS −VT( )
BJT operation: gamma
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n+ emitter
p base
n collector
n+
FB RB IE ICIEn
IEpIE = IEn + IEp
IEn
IC ≈ IEn
IB = IEp
IEn = qAEni2
NAB
⎛⎝⎜
⎞⎠⎟DnWB
eqVBE /kBT −1( ) ≈ IC
IEp = qAEni2
NDE
⎛⎝⎜
⎞⎠⎟DpWE
eqVBE /kBT −1( ) ≈ IBγ = IEn
IEn + IEp< 1
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BJT operation: base transport factor
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n+ emitter
p base
n collector
n+
FB RB IE ICIEn
IEpIE = IEn + IEp
ICn
IC ≈ IEn
IB = IEp
IEn = qAEni2
NAB
⎛⎝⎜
⎞⎠⎟DnWB
eqVBE /kBT −1( )
IEp = qAEni2
NDE
⎛⎝⎜
⎞⎠⎟DpWE
eqVBE /kBT −1( ) ≈ IB
ICn = αT IEn ≈ IC
BJT operation: IE and IC
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n+ emitter
p base
n collector
n+
FB RB IE ICIEn
IEpIE = IEn + IEp
ICn
IC ≈ IEn
IB = IEp
ICn = αT IEn = IC
γ = IEnIEn + IEp
=IEnIE
IC = αT IEn = αTγ IE = αdcIE
IB = IE − IC = IC β
IC = αdcIE
αdc = αTγ
β = αdc1−αdc
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common emitter (active region)
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IC
IB VCE
VBE
VCB
IE
IC = βIB
IB VCE >VBE
IE = β +1( ) IB
VBE > 0
IV characteristics
Gummel plot
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log J( )
VBE
JC = JC0 eqVBE /kBT −1( )
JB = JB0 eqVBE /nkBT −1( )
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NPN bipolar transistor
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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
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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
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BJT operation: saturation region
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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
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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
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BJT operation: inverted active region
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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)
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1) Base recombination (base transport factor)
2) Speed (frequency response)
3) Base width modulation (Early effect)
4) Typical doping profiles
5) Kirk effect
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base recombination
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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( )WB2τ nIEn
⎛
⎝
⎜⎜⎜⎜
⎞
⎠
⎟⎟⎟⎟
IEn = qAEDnΔn 0( )WB
αT ≈ 1−12
WBLn
⎛⎝⎜
⎞⎠⎟
2
speed (base transit time)
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0 x
Δn x( )
Δn 0( )
WB
Δn WB( ) ≈ 0
IEn
quasi-neutral base
ICn ≈ IEn
IC = qAEDnΔn 0( )WB
IC =QBtt
QB =qΔn 0( )WB
2
tt =WB
2
2Dn
fT =12πtt
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effects of saturation on speed
35 Pierret, Fig. 12.7
Early effect (base width modulation)
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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)?
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Early effect (base width modulation)
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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
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n+ emitter
p base
n collector
n+
FB RB IEn
IEp
IEn ∝ni2
NAB
IEp ∝ni2
NDE
γ = IEnIEp + IEn
≈1
1+ NABNDE
⎛⎝⎜
⎞⎠⎟
Emitter must be doped more heavily than the base.
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HBT
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n+ emitter
p base
n collector
n+
FB RB
EGE EGB EGC
IEn
IEp
IEn ∝niB2
NAB
IEp ∝niE2
NDE
γ = IEnIEp + IEn
≈1
1+ niE2
niB2NABNDE
⎛⎝⎜
⎞⎠⎟
Freedom to dope the base heavily
collector doping
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n+ emitter
p base
n coll
n+
FB RB IEn
IEp
ρ = qNDJC = qDnWB
Δn 0( )
JC = qnυsatn ≈ ND
“base push out” Kirk effect
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common base (active region)
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IC
IB VCE
VBE
VCB
IE
IC = αdcIE
VCB > 0VEB < 0
IE
IB = IC β
IV characteristics
common base (active region)
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IC
VCBVEB IB
IE
BE: FB BC: RB
VEB < 0VCB > 0
Pierret, Fig. 10.4
active
cut-off
saturation