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Semiconductor Physics
Chapter 5, Bipolar transistors
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David Krapohl
Department of Information Technology and Media
Mid Sweden University
April 27, 2011
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Outline
…or table of contents
1.
Static characteristics
Symbols and nomenclature: npn- and pnp-transistors
Biasing configurations
2.
Output Characteristics
3.
Nonideal Effects
Emitter bandgap narrowing
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Static characteristics
Symbols and nomenclature: npn- and pnp-transistors
Emitter Base Collector
IE
.
n+
p
n
Emitter Base Collector
IB
IE
.
p+
IB
E
.
IC
IB
E
C
B
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p
n
.
C
B
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Static characteristics
Biasing configurations
.
-
VBE
+
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IC
IE
Common-Base
+
IB
VCB
-
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Static characteristics
Biasing configurations
IC
+
.
IB
.
VCB
+
VBE
-
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IE
Common-Emitter
-
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Static characteristics
Biasing configurations
IE
-
.
IB
.
VCE
VCB
+
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IC
Common-Collector
+
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Static characteristics
Connection and biases in common-base configuration
Emitter Base
p
n+
.
IE
InE
IpE
IrE
Collector
n
InC
IrB
IC
Output
ICO
VBE
IB
Depletion
VCB
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Static characteristics
Doping profiles and critical dimensions
−
N+
D − NA
NE
0
−xE
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WE
NC
W
WDC
NB
WB
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WC
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Static characteristics
Energy band diagram of a npn transistor
−InE
IrB
EF
IrE
−InC
−ICO
IpE
EC
ICO
EF
.
EV
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Electron currents
Emitter and collector edge
np − npo
d2 np
+ Dn 2
τn
dx
( )
( )
x
−x
np (x) = npo + C1 exp
+ C2 exp
Ln
Ln
√
C1 and C2 are constants and L≡ Dn τn
0 = −
{
(
)}
[
]
−W
W
np (W) − npo − np (0) − npo exp
/2 sinh
Ln
Ln
{
( )
}
[
]
]
W [
W
=
np 0 − npo exp
np (W) − npo /2 sinh
Ln
Ln
C1 =
C2
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Electron currents
Emitter and collector edge
Boundary conditions for the two edges of the base:
(
)
qVBE
np (0) = npo exp
kT
(
)
qVBC
np (W) = npo exp
kT
(
)
AE qDn npo
W
qVBE
InE =
coth exp
Ln
Ln
kT
(
)
AE qDn npo
W
qVBE
InC =
cosech exp
Ln
Ln
kT
The ratio of InC /InE is called base transport factor αT
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Electron currents
Emitter and collector edge
InE ≈ InC
AE qDn npo
≈
exp
W
(
qVBE
kT
)
AE qDn n2i
≈
exp
WNB
(
qVBE
kT
)
.
Can be reduced to:
InE ≈ InC ≈
2AE DN QB
W2
QB is the injected excess charge in the base:
∫
QB = q
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W
[np (x) − npo ]dx
0
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Doping profile
1021
1020
Emitter
n+
.
Base
WB
Collector
n+
WC
p
1018
1017
n
1016
1015 .
0
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0.2
0.3
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Electron Currents
A build-in electric field enhances electron transport.
(
)
Ei − EF
p(x) ≈ NB (x) = ni exp
kT
built-in field
E (x) =
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dEi
kT dNB
=
qdx
qNB dx
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Electron Currents
(
)
dnp
In (x) = AE q µn µp E + Dn
dx
substituting E
(
In (x) = AE qDn
np dNB dnp
+
NB dx
dx
)
steady state solution with boundary condition np (W) = 0
In (x)
np (x) =
AE qDn NB (x)
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∫
W
NB (x)dx
x
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Electron Currents
total impurity dose per area in the base
.
∫
N‘b
≡
W
NB (x)dx
x
called Gummel number. (Si: 1012 to 1013 cm−2 )
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Hole Currents
diffusion current injected from base to emitter
.
IpE
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(
)
]
[
AE qDp EpnoE
qVBE
=
exp
−1
WE
kT
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Recombination
• Shockley-Read-Hall recombination
• Auger recombination
.
1
1
1
=
+
τ
τn τA
Base-emitter recombination
IrE
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1
∝ exp
τ
(
qVBE
mkT
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Collector base junction
.
(
ICO ≈ AC q
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DpC pnoC
Dn npo
+
WC − WDC
W
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Current gain
IE = InE + IrE + IpE
.
IC = InC + ICO
IB = IpE + IrE + (InE − InC ) − ICO
It holds true that
IE = IC + IB
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Parameters for a bipolar transistor
Parameters for a Bipolar Transistor
Emitter injection efficiency
Base transport factor
Common-base current gain, hFB
“
small signal hfb
Common-emitter current gain, hFE
“
small signal hfe
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γ ≡ InE /IE
αT ≡ InC /InE
α0 ≡ InC /IE = γαT ≈ IC /IE
α ≡ dIC /dIE
β0 ≡ α0 /(1 − α0 ) ≈ IC /IB
β ≡ dIC /dIE
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Parameters for a bipolar transistor
Common base current gain
ICBO
α0 ≡ hFB =
IC − ICB0
InC
InC InE
=
=
= αT γ
IE
IE
In E IE
γ is defined as emitter injection efficiency
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Parameters for a bipolar transistor
Common emitter configuration
IC = β0 IB + ICEO
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ICEO is ICO when IB = 0, or open base:
IC
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α0 (IB + ICO ) + ICBO
ICBO
α0
IB +
=
1 − α0
1 − α0
α0
⇒ β0 ≡ hFE =
1 − α0
=
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Parameters for a bipolar transistor
Base transport factor, emitter injection efficiency
Base transport factor
.
αT ≡
InC
1
W
=
≈1− 2
InE
cosh(W/Ln )
2Ln
Emitter injection efficiency
[
( )]−1
pnoE DpE Ln
InE
InE
W
γ≡
≈
≈ 1+
tanh
IE
InE + IpE
NPO Dn WE
Ln
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hFE =
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npo Dn WE
γ
=
coth
1−γ
pnoE DpE Ln
(
W
Ln
)
∝
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npo
NE
NE
∝
∝ ‘
pnoE W
NB W
Nb
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Output Characteristics
1.
applied voltages control the boundary densities through the
term exp(qv/kT)
2.
emitter and collector currents are given by minority density
gradients at x=0 and x=W (junction boundaries)
3.
base current is the difference between emitter and collector
current
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Nonideal Effects
Emitter bandgap narrowing
To improve hFE , the emitter should be much more heavily doped
than the base, that is NE >> NB .At high doping concentrations
bandgap narrowing has to be considered.
Bandgap reduction:
)
(
N
∆Eg = 18.7 ln
7 · 1017
N larger than 7 · 1017 Intrinsic carrier density in the emitter is:
(
)
)
(
Eg − ∆Eg
∆Eg
2
2
niE = NC NV exp −
= ni exp
kT
kT
ni : intrinsic carrier density
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Nonideal Effects
Emitter bandgap narrowing
Minority carrier concentration becomes
(
)
∆Eg
n2iE
n2i
pnoE =
=
exp
NE
NE
kT
Increased minority carrier concentration in the emitter.
The net result is an increased hole diffusion current and the current
gain is recuded
(
)
npo
∆Eg
hFE ∝
∝ exp −
pnoE
kT
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Nonideal Effects
Kirk Effect
In modern bipolar transistors with a lightly doped collector region,
the net charge is changed significantly under high-current condition.
The high-field region is relocated from the base-collector junction
towards the n+-substrate.
It is referred to as the Kirk effect and increases the effective Gummel
number and causes a reduction of hFE (current gain).
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Nonideal Effects
Current Crowding
Minimization of the emitter resistance results in non-uniform current
passing through the emitter area.
.
Sef effective width carries most of the current.
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