Klimeck – ECE606 Fall 2012 – notes adopted from Alam ECE606: Solid State Devices Lecture 18 Bipolar Transistors a) Introduction b) Design (I) Gerhard Klimeck [email protected]1 Klimeck – ECE606 Fall 2012 – notes adopted from Alam Background 2 Point contact Germanium transistor Ralph Bray from Purdue missed the invention of transistors. http://www.electronicsweekly.com/blogs/david-manners-semiconductor-blog/2009/02/how-purdue-university-nearly-i.html http://www.physics.purdue.edu/about_us/history/semi_conductor_research.shtml Transistor research was also in advanced stages in Europe (radar). E C Base! E B C
29
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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Background
2
Point contact Germanium transistor
Ralph Bray from Purdue missed the invention of transistors.http://www.electronicsweekly.com/blogs/david-manners-semiconductor-blog/2009/02/how-purdue-university-nearly-i.htmlhttp://www.physics.purdue.edu/about_us/history/semi_conductor_research.shtml
Transistor research was also in advanced stages in Europe (radar).
E C
Base!
E B C
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Shockley’s Bipolar Transistors …
n+emitter
pbase
ncollector
n+
Double
Diffused BJT
p basen-collector
n+
n+
n+ emitter
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Modern Bipolar Junction Transistors (BJTs)
4
SiGe Layer
Transistor speed increases as the electron's travel distance is reduced
SiGe intrinsic base Dielectric trench
N+P+N
P-
N-
CollectorEmitterBaseN+
Why do we need all these design?
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Symbols and Convention
5
Poly emitter
Low-doped base
Collector dopingoptimization
N+
P
N
Symbols
NPN PNP
Collector
Emitter
Base
Collector
Emitter
Base
IC+IB+IE=0
VEB+VBC+VCE=0
E
B
C
(DC)
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Outline
6
1) Equilibrium and forward band-diagram
2) Currents in bipolar junction transistors
3) Eber’s Moll model
4) Intermediate Summary
5) Current gain in BJTs
6) Considerations for base doping
7) Considerations for collector doping
8) Conclusions
REF: SDF, Chapter 10
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Topic Map
7
Equilibrium DC Small signal
Large Signal
Circuits
Diode
Schottky
BJT/HBT
MOS
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Band Diagram at Equilibrium
8
1P P P
pr g
t q
∂ = − ∇ • − +∂
J
( )D AD q p n N N+ −∇ • = − + −
P P Pqp E qD pµ= − ∇J
1N N N
nr g
t q
∂ = ∇ • − +∂
J
J µ= + ∇N N Nqn E qD n
Equilibrium
DC dn/dt=0Small signal dn/dt ~ jωtn
Transient --- Charge control model
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Band Diagram at Equilibrium
9
BaseEmitter Collector
Vacuum level
EC
EV
EF
χ2
χ1 χ3
NPN homojunction BJT
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Electrostatics in Equilibrium
10
( )0
,
2 s Bn E bi
E B E
k Nx V
q N N N=
+ε
( )0
,
2 s Ep BE bi
B E B
k Nx V
q N N N=
+ε
( )0
,
2 s Bn C bi
C C B
k Nx V
q N N N=
+ε
( )0
,
2 s Cp BC bi
B C B
k Nx V
q N N N=
+ε
BaseEmitter Collector
Two back to back p-n junction
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Outline
11
1) Equilibrium and forward band-diagram
2) Currents in bipolar junction transistors
3) Eber’s Moll model
4) Intermediate Summary
5) Current gain in BJTs
6) Considerations for base doping
7) Considerations for collector doping
8) Conclusions
REF: SDF, Chapter 10
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Topic Map
12
Equilibrium
DC Small signal
Large Signal
Circuits
Diode
Schottky
BJT/HBT
MOS
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Band Diagram with Bias
13
1P P P
pr g
t q
∂ = ∇ • − +∂
J
( )D AD q p n N N+ −∇ • = − + −
P P Pqp E qD pµ= − ∇J
1N N N
nr g
t q
∂ = ∇ • − +∂
J
J µ= + ∇N N Nqn E qD n
Non-equilibrium
DC dn/dt=0Small signal dn/dt ~ jωtn
Transient --- Charge control model
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Electrostatics in Equilibrium
14
( ) ( )0,
2 s Bn E bi EB
E B E
k Nx V V
q N N N
ε= −+
( ) ( )0,
2 s Ep BE bi EB
B E B
k Nx V V
q N N N
ε= −+
( ) ( )0,
2 s Bn C bi CB
C C B
k Nx V V
q N N N
ε= −+
( ) ( )0,
2 s Cp BC bi CB
B C B
k Nx V V
q N N N
ε= −+
BaseEmitter Collector
VEB VCB
Assume current flow is small…fermi level is flat
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Current flow with Bias
15
EC-Fn,C
Fp,B-EV
EC-Fn,EV
Input small amount of holes results in large amount of electron output
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Vg↑
Modern MOSFET - “Fundamental” Limitlooks similar to BJT
p
Metal
n+ n+
Oxide
DSVg
x
E
S≥60 mV/dec
Threshold
VgVdd
log Id
0
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Vg↑
Modern MOSFET - “Fundamental” Limitlooks similar to BJT
p
Metal
n+ n+
Oxide
DSVg
x
E
S≥60 mV/dec
Threshold
VgVdd
log Id
0
DOS(E), log f(E)
Ef
`̀
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Coordinates and Convention
18
BaseEmitter Collector
N+ P N
0 WX’’ X’X
, , ,
0 0 0 0 0 0
, . . . . , . . . .
, . . . . . . . . , . . . . . .
, . . . . . . . , . . . . . .
E D E B A B C D C
E P B N C P
E p B n C p
N N N N N N
D D D D D D
n n p p n n
= = == = == = =
Doping
Minority carrier diffusion
Majority carriers
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Carrier Distribution in Base
19
( )2,(0 ) 1BEi B qV
B
nn e
Nβ+∆ = − ( )
2,( ) 1BCi B qV
BB
nn x W e
Nβ∆ = = −
( ) ( )2,
2,1) 1( 1BE BCi B qV
B
B
B
i qV
B B
x xn x
W W
ne
ne
N Nβ β
∆ = − +
−
−
VEBVCB
( ) 1B B
x xn x Ax B
W WDC
∆ = + = − +
DC
Assume no recombination. Start from minority carrier
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Collector and Emitter Electron Current
20
( ) ( )2,
2,1) 1( 1BE BCi B qV
B
B
B
i qV
B B
x xn x
W W
ne
ne
N Nβ β
∆ = − +
−
−
( ) ( )2,
,
2, 1 1BBE
B
Ci B qVn i B qn C
Vn
BBn
BW B
nqDe
W
dnJ qD
dx
nqDe
W NNββ= = −− −+
( )
,
2
1BE
p E p
p qVi
n D
dpJ qD
dxD n
eW N
β
= −
= − −
VBE
VBE
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Current-Voltage Characteristics
21
JC
VCE
IB
VBE
log10 JC
> 60 mV/dec.
High-level injectionseries resistance, etc.
Normal, Active RegionEB: Forward biasedBC: Reverse biased
( ) ( )2 2, ,
, 1 1BCBEi B i B qVqVn nn C
B B B B
n nqD qDJ e e
W N W N= − − + −ββ
WB is not independent of bias=> Early Effect same physics of diode , rollover
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Outline
22
1) Equilibrium and forward band-diagram
2) Currents in bipolar junction transistors
3) Eber’s Moll model
4) Intermediate Summary
5) Current gain in BJTs
6) Considerations for base doping
7) Considerations for collector doping
8) Conclusions
REF: SDF, Chapter 10
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Ebers Moll Model
23
( )( )
0
0
1
1
BE
BC
qVF F
qVR R
I I e
I I e
β
β
= −
= −
IC=Ic,n+Ic,p
( ) ( )
( ) ( )
2 2 2, , ,
0 0
1 1
1 1
BCBE
BCBE
pi B i B i C qVqVn n
B B B B C C
qVqVF F R
C
qDn n nqD qDI A e A e
W N W N W N
I e I e
ββ
ββα
= − − + + −
≡ − − −
( ) ( )
( ) ( )
2 2 2, , ,
0 0
1 1
1 1
BCBE
BCBE
p i E i B i B qVqVn n
E E B B E B
qVqVF R
E
R
qD n n nqD qDA e A e
W N W N W N
I e I e
I ββ
ββ α
= − + − + −
≡ − − −
IE
IF
IB
IC
E
B
C
IR
αFIF
αRIR
Hole diffusion in collector
IE=IE,n+IE,p
Temperature dependent
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Common Base Configuration
24
P NE
IE ICC
BB
VEB(in)
VCB(out)
How would the model change if this was a Schottky barrier BJT?
IE
IF
IB
IC
E
B
C
IR
CBE CBC
αRIR αFIFN
Junction capacitance and diffusion capacitance
The original transistor was a metal/ semicond / metal deviceNo minority carriers, no diffusion capacitance but the “rest” about the same.
Common base configuration provides power gain, but no current gain. => Emitter and collector current are identical => no current gain=> Collector current IC can be driven through large resistor => power gainIs there another configuration that can deliver current gain?
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Common Emitter Configuration
25
αRIR
αFIF
CBE
CBC
E
BIB
IE
IC
IF
IR
( )1
1
F F F FF F B
FF
F
I II I= = − =
−
α α ααβα
F F
F
Iαβ
F F R RI I−α α
Cµ
Cπ
IR
P+
N
P
C
E E
B
VEB(in)
VEC(out)
ICIB
This is a practice problem …
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Intermediate Summary
26
• The physics of BJT is most easily understood with
reference to the physics of junction diodes.
• The equations can be encapsulated in simple
equivalent circuit appropriate for dc, ac, and large
signal applications.
• Design of transistors is far more complicated than this
simple model suggests => the next lecture elements
• For a terrific and interesting history of invention of the
bipolar transistor, read the book “Crystal Fire”.
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Outline
27
1) Equilibrium and forward band-diagram
2) Currents in bipolar junction transistors
3) Eber’s Moll model
4) Intermediate Summary
5) Current gain in BJTs
6) Considerations for base doping
7) Considerations for collector doping
8) Conclusions
REF: SDF, Chapter 10
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Ebers Moll Model
28
IE
IF
IB
ICE
B
C
IR
αFIFαRIR
( )( )
0
0
1
1
BE
BC
qVF F
qVR R
I I e
I I e
= −
= −
β
β
( ) ( )
( ) ( )
2, , ,
00
2 2
1 1
1 1
BCB
BE
E
BC
pi B i E i B qVqVn nE E E
B B E E
qVR R
V
B
F
B
q
qDn n nqD qDI A e A
I e
eW N W N W N
I e β β
ββ
α
= − + − + −
= − −−
( ) ( )
( ) ( )
2 2 2, , ,
0 0
1 1
1 1
BCBE
BCBE
i B i B i C qVqVn n nC C C
B B B B C C
qVqVF F R
n n nqD qD qDI A e A e
W N W N W N
I e I e
ββ
ββα
= − − + + −
= − − −
( ) ( )2 2, ,1 1BCBEp pi E i C qVqV
BE E C C
qD qDn nI A e A e
W N W Nββ= − + −
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Ebers Moll Model (Basic definition)
29
IB IC
0 VCE
saturationregion
active region
The Ebers-Moll model describes both the active and the saturation regions of BJT operation.
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Gummel Plot and Output Characteristics
30
• The simultaneous plot of collector and base current vs.the base-emitter voltage on a semi-logarithmic scale isknown as a Gummel Plot.
• This plot is extremely useful in device characterizationbecause it reflects on the quality of the emitter-basejunction while the base-collector bias is kept at aconstant.
• A number of other device parameters can be ascertainedeither quantitatively or qualitatively directly from theGummel plot because of its semi-logarithmic nature
− For example the d.c gain β, base and collector idealityfactors, series resistances and leakage currents.
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Gummel Plot and Output Characteristics
31
2 2, , //( 1) ( 1)BCBEi B i B q kTq kTn n
B B B B
C VVn nqD qDe e
A W N W N
I − − + −≃
2, /( 1)BEp i E V kT
E E
B qqD ne
A W N
I = −
CDC
BI
Iβ =
DCβ Common emitter Current Gain
VBE
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Current Gain
32
P+
N
P
C
E E
B
VEB(in)
ICIBCommon Emitter current gain ..
CDC
B
I
Iβ =
2 2( / )/, ,
2/,
( 1) ( 1)
( 1)
BCBE
BE
qV kTqV kTi B i Bn n
B B B B
qV kTi En
E E
n nqD qDe e
W N W N
nqDe
W N
− + −=
−
2,
2,
i Bn E E
B p i E B
nD W N
W D n N≈
Common Base current gain ..P+ N P
E
IE IC
C
BB
VEB(in)
VCB(out)
CDC
E
I
Iα = C C
DC
B E C
I I
I I Iβ = =
− 1DC
DC
αα
=−
DC transfer gain
Will examine
Properties are related – (transistor did not change ☺)
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Current Gain
33
2,
2,
i Bn E EDC
B p i E B
nD W N
W D n Nβ ≈
Hig
h in
ject
ion
colle
ctor
cur
rent
=>
roll-
off
Bas
e cu
rren
t do
es n
ot r
oll o
ff
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
How to make a Good Silicon Transistor
34
Emitter doping higherthan Base doping
Base doping hard to controlEmitter doping easier
~1, same materialprimarily determined by bandgap
Make-Base short …(few mm in 1950s, 200 A now)Want high gradient of carrier density
For a given Emitter length
2,
2,
i Bn E EDC
B p i E B
nD W N
W D n Nβ ≈
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Doping for Gain …
35
NE
NB
NC
N+
P
N
2,
2,
i Bn E EDC
B p i E B
nD W N
W D n Nβ ≈
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Outline
36
1) Equilibrium and forward band-diagram
2) Currents in bipolar junction transistors
3) Eber’s Moll model
4) Intermediate Summary
5) Current gain in BJTs
6) Considerations for base doping
what’s wrong with the previous recipe?
7) Considerations for collector doping
8) Conclusions
REF: SDF, Chapter 10
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Problem of Low Base Doping: Current Crowding
37
( )
( )
' ( )
' ( )
2,
2,
1( )
( )1
BE
BE
qi Bn V
CC B B
p qi EB B
E E
x
V x
nqDe dxJ x dxI W N
qD nI J x dxe dx
W N
β
β
β−
= = =−
∫∫∫ ∫
p base
n-collector
n+
n+VBE
VBEDouble diffused junction configuration:Emitter doping must compensate / overcome the base doping
Low doping in base=> resistance along the current path=> potential drop
=> Determines the injection => Spatially dependent=> More current in the corners
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Low Base Doping: Non-uniform Turn-on
38
n+ p base
n-collectorn+
B
E
Interdigitated designs for almost all high power transistors (E-B distance minimized)
Non-uniform current inefficientHigh current at the edge can cause burn-out
Sketches from text book
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Low Base Doping: Current Crowding
39
p base
n-collector
n+
n+VBE
We talked about how low doping for the base enhances the current gain.
But there is a potential downside to this approach
If the base doping is kept to small values, it will have a high resistance: Lesser ability to conduct means higher resistance
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Low Base Doping: Current Crowding
40
p base
n-collector
n+
n+VBE
Non-zero base resistance results in a lateral potential difference under the emitter region
For an n-p-n transistor as shown, the potential decreases from edge of the emitter towards the centre (the emitter is highly doped and can be considered an equipotential region)
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Low Base Doping: Current Crowding
41
p base
n-collector
n+
n+VBE
The number of electrons injected from emitter to base is exponentially dependent on base-emitter voltage
With the lateral drop in the voltage in the base between the edge and centre of emitter, more carriers will be injected at the edge than the emitter centre.
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Low Base Doping: Current Crowding
42
Key facts:
1. Current crowding is due to 2D nature of BJTs
2. It is a function of the doping concentration
3. As doping concentration increases, resistivity decreases
− Consequence: Current gain goes smaller � Emitter current injection efficiency decreases
The larger current density near the emitter may cause localized heating and high injection effects
Possible Solution: Emitter widths are fabricated with an inter-digitated design � Many narrow emitters connected in parallel to achieve the required emitter area
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Low Base Doping: Non-uniform Turn-on
43
n+ p base
n-collectorn+
B
E
Interdigitated designs for almost all high power transistors (E-B distance minimized)
Non-uniform current inefficientHigh current at the edge can cause burn-out
Sketches from text book
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Problem of Low Base Doping: Punch-through
44
NE
NB
NC
( ) ( )0,
2 s Ep BE bi BE
B E B
k Nx V V
q N N N= −
+ε
( ) ( )0,
2 s Cp BC bi BC
B C B
k Nx V V
q N N N= −
+ε
NN+
Low base doping is not a good idea!
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Problem of low Base-doping: Base Width Modulation
45
2,
2,, ,
E i Bn EDC
p i EB p B p c B
D W n N
W x x D n Nβ ≈
− −
N+
P N
( ) ( )0,
2 s Ep BE bi BE
B E B
k Nx V V
q N N N= −
+ε
( ) ( )0,
2 s Cp BC bi BC
B C B
k Nx V V
q N N N= −
+ε
Gain depends on collector voltage (bad) …Depletion region width modulation
NB
NC
NE
Electrical base region is smaller than the metallurgical region!
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Problem of Low Base-doping: Early Voltage
46
2,
2. . ,
i Bn E EDC
p B p C i EB p B
D W n N
W x x D n Nβ ≈
− −
2 2, ,( / ) ( / )
, ( 1) 1' '
( )BE BCi B i BqV kT qV kTn nn
BC
B B B
qD n qD nI e e
NW W N= − − + −
C C C
BC BC A A
dI I I
dV V V V= ≈
+
VBC
VA
IC
Ideally
In practice
VBC about 1VVA ideally infinity
Jim Early device pioneer
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
The Early Voltage PS1
47
VA
VBC
IC
Ideally
In practice
• The collector current depends on VCE:
• For a fixed value of VBE, as VCE increases, the reverse bias on the collector-base junction increases, hence the width of the depletion region increases.
− The quasi-neutral base width decreases � collector current increases.
Due to the Early effect, collector current increases with increasing VCE, for a fixed value of VBE.
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
The Early Voltage PS2
48
VA
VBC
IC
Ideally
In practice
• The Early voltage is obtained by drawing a line tangential to the transistor I-V characteristic at the point of interest.
• The Early voltage equals the horizontal distance between the point chosen on the I-V characteristics and the intersection between the tangential line and the horizontal axis.
• Early voltage is indicated on the figure by the horizontal dotted line
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Punch-through and Early Voltage
49
C C
B A
B BA
CB
C
B
B I I
q W V
W
C
N
qNV
C
− ≈
⇒ = −
C C C
BC BC A A
dI I I
dV V V V= ≈
+
Need higher NB and WB or …
( ) ( )2 2, ,1 1BCBEi B i B qVqVn n
CB B B B
n nqD qDI e e
W N W Nββ= − + −
( )( )
1
C C
BC B
B B
B
B BC
C
B BCB
ddI dI
dV d q W dV
dI d
q
qN W
Q
dW dV
N
N
=
=
∞→
1 C
BCB
BqN
IC
W
= −
2C
B B B B
dI d
dW dW W W
ξ ζ = = −
C
B
I
W= −
BW
ξ=
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Outline
50
1) Equilibrium and forward band-diagram
2) Currents in bipolar junction transistors
3) Eber’s Moll model
4) Intermediate Summary
5) Current gain in BJTs
6) Considerations for base doping
7) Considerations for collector doping
8) Conclusions
REF: SDF, Chapter 10
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Collector Doping
51
2,
2, , ,
i Bn E E
B p B p C p i E B
nD W N
W x x D n N≈
− −β
0
, ,
sCB
n C p B
Cx x
=+
κ ε
If you want low base dopingthen reduce collector doping even more to increase Collector depletion…..
B BA
CB
qN WV
C= −
N+
P N
NB
NC
NE
Base-Collector in reverse bias⇒Majority carriers only⇒No diffusion capacitance
⇒Reduce capacitance⇒Increase xnC
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
… but (!) Kirk Effect and Base Pushout
52
+
-
Nc
NB
WCWB
p-Base n-Collector
n+
xSpa
ce-C
harg
e D
ensi
ty
Nc
NB
WCWB
p-Base n-Collectorn+
xSpa
ce-C
harg
e D
ensi
ty
B B C CN x N x=
2 2
02bi BC B B C Cs
qV V N x N x − = + κ ε
( ) ( )2 2
0
' '2bi BC B B C C
s
qV V N n x N n x − = + + − κ ε
( ) ( )' 'B B C CN n x N n x+ = −
'
11
1 1
C
sat BBC C C
C
C sat C
J
q NNx x x
N q N
n
n Jυ
υ
++= =
− −
C satnJ qυ=Additional charge!Can be large compared to low doping
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Kirk Effect and Base Pushout
53
n+emitter
pbase
ncollector
n+
x
Nc
NB
p-Base n-Collector n+
Spa
ce-C
harg
e D
ensi
ty
WCWB
n+
x
Nc
NB
p-Base n-Collector
Spa
ce-C
harg
e
WCWB
p-Base n-Collector n+
x
Spa
ce-C
harg
e
WCWB
WCIB WS
C
nc-Nc
E
⇒Increase bias & current
⇒Junction lost⇒High current dominates collector doping
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Kirk Effect and Base Pushout
54
'
1
1
C
sat BC
sat
CC
C
J
q N
J
q Nx x
υ
υ
−
+=
,C crit sat C KJ q N Jυ= ≡
Can not reduce collector doping arbitrarily without causing base pushout
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Kirk Effect
The Kirk effect occurs at high current densities in a bipolar transistor. The effect is dueto the charge density associated with the current passing through the base-collectorregion. As this charge density exceeds the charge density in the depletion region thedepletion region ceases to exist. Instead, there will be a build-up of majority carriersfrom the base in the base-collector depletion region. The dipole formed by thepositively and negatively charged ionized donors and acceptors is pushed into thecollector and replaced by positively charged ionized donors and a negatively chargedelectron accumulation layer, which is referred to as base push out. This effect occurs ifthe charge density associated with the current is larger than the ionized impuritydensity in the base-collector depletion region. Assuming full ionization, this translatesinto the following condition on the collector current density.
Key point : Under high current and low collector doping the depletion approximation is invalid in the C-B junction!
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Perhaps High Doping in Emitter?
56
2,
2,
i Bn E
B p i E B
EnD W
W D n
N
Nβ ≈
Band-gap narrowing reduces gain significantly …
(Easki-like) Tunneling cause loss of base control …
,
,
/
/
B
g E
gE kT
n C VE
B p BC V
EE
kT
D N NW e
W D N e NN
N−
−= /gE kT E
B
Ne
N−∆≈
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Summary
57
While basic transistor operation is simple, its optimum design is not.
In general, good transistor gain requires that the emitter doping be larger than base doping, which in turn should be larger than collector doping.
If the base doping is too low, however, the transistor suffers from current crowding, Early effects. If the collector doping is too low, then we have Kirk effect (base push out) with reduced high-frequency operation and if the emitter doping is too high then the gain is reduced.