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Klimeck – ECE606 Fall 2012 – notes adopted from Alam
ECE606: Solid State DevicesLecture 19
Bipolar TransistorsDesign
Gerhard [email protected]
1
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Outline
2
1) Current gain in BJTs
2) Considerations for base doping
3) Considerations for collector doping
4) Intermediate Summary
5) Problems of classical transistor
6) Poly-Si emitter
7) Short base transport
8) High frequency response
9) Conclusions
REF: SDF, Chapter 10
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
Current flow with Bias
5
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
Gummel Plot and Output Characteristics
6
CDC
BI
Iβ =
DCβ Common emitter Current Gain
VBE
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
How to make a Good Silicon Transistor
7
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
Electrostatics in Equilibrium
8
( )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
Electrostatics in Equilibrium
9
( ) ( )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
Problem of Low Base Doping: Punch-through
10
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!
VBE is positive (forward bias) VBC is negative (reverse bias) => xp,BC grows
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Problem of low Base-doping: Base Width Modulation
11
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
The Early Voltage
12
• 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.
collector current increases with increasing VCE, for a fixed value of VBE.
VA
VBC
IC
Ideally
In practice
Gain depends on collector voltage (bad) …Depletion region width modulation
Device PioneerJim Early
VBC about 1VVA ideally infinity
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
The Early Voltage
13
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
Device PioneerJim Early
VBC about 1VVA ideally infinity
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Problem of Low Base-doping: Early Voltage
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= ≈
+
Device PioneerJim Early
VA
VBC
IC
Ideally
In practice
VBC about 1VVA ideally infinity
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Punch-through and Early Voltage
15
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
16
1) Current gain in BJTs
2) Considerations for base doping
3) Considerations for collector doping
4) Intermediate Summary
5) Problems of classical transistor
6) Poly-Si emitter
7) Short base transport
8) High frequency response
9) Conclusions
REF: SDF, Chapter 10
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Collector Doping
17
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
18
+
-
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
19
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
20
'
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
,
,
/
/
B
g E
gE kT
n C VE
B p BC V
EE
kT
D N NW e
W D N e NN
N−
−=
Perhaps High Doping in Emitter?
22
2,
2,
i Bn E
B p i E B
EnD W
W D n
N
Nβ ≈
Band-gap narrowing reduces gain significantly …
/gE kT E
B
Ne
N−∆≈
Very high doping can narrow the bandgap of a semiconductor!
If the emitter is extremely highly doped, then the bandgap in the emitter may be smaller than the base
=> Reduction in gain
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Perhaps High Doping in Emitter?
23
(Easki-like) Tunneling cause loss of base control …
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Intermediate Summary
24
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.
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Outline
25
1) Current gain in BJTs
2) Considerations for base doping
3) Considerations for collector doping
4) Intermediate Summary
5) Problems of classical transistor
6) Poly-Si emitter
7) Short base transport
8) High frequency response
9) Conclusions
REF: SDF, Chapter 10
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Doping for Gain
26
2,
2,
i Bn E Edc
B p i E B
nD W N
W D n Nβ ≈
NE
NB
NC
Emitter doping: As high as possible withoutband gap narrowing
Base doping: As low as possible, withoutcurrent crowding, Early effect
Collector doping: Lower than base dopingwithout Kirk Effect
Base Width: As thin as possible withoutpunch through
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
How to make better Transistor
27
2,
2,
i Bn E E
B p i E B
nD W N
W D n Nβ ≈
Classical Shockley Transistor
Hetero-junction Bipolar Transistor
Graded Base transport
Polysilicon Emitter
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Poly-silicon Emitter
28
N+
P N
SiGe intrinsic base Dielectric trench
N+P+N
P-
N-N+
CollectorEmitterBase
N+
Poly-silicon
emitter
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Poly-silicon Emitter
29
1, ,
22p E pol s
E
y p
pI q qD
W
ppυ−= − = −
( )2,
, 1 1 1BEi B qVnn E
B B
nqDI n n e
W N= ≡ −β
N+ P
1
2 p E
p E s
D W
Dp W
p
υ=
+
, , 2 1p E
p E pp
o ys
ssE
lID
q p qpW
D W
υυ
υ= − = −
+×
( ), , 1pp si EEI Dq W p= −
, ,
, ,
p E poly
p E si p
s
sE
I
DI W
υυ
=+
WE
poly
p2p1
vs
Question: Why does poly only suppress the hole current, not electron current?
Ans. Polysilicon is not a ohmic contact and acts as rectifying contact. It blocks the easy passage of holes but lets electrons
pass through
vs Infinite at metal
Finite at poly
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Gain in Poly-silicon Transistor
30
, , 1 , ,p E poly p B pols
s
p E
Ey
p
D WI p
Wq I
D
υυ
×= − =
+
( ), , 1pp si EEI Dq W p= −
, , ,
, , ,
p B poly B poly
p B s p BE
s
ssi iD
I I
I IW
υυ
=+≃
,
, ,,B si
B siC Cpoly
B poly B polyI
II I
I Iβ
= = ×
Poly suppresses base current, increases gain …
2,2,
( )1
si Bn E
B i Ep
sE
B
nD N
W n ND Wυ
υ→ × <<∵
2,
2,
i Bn E E
B p i E B s
p sEnD W N
W D n N
D W υυ
+ ≈ ×
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Outline
31
1) Current gain in BJTs
2) Considerations for base doping
3) Considerations for collector doping
4) Intermediate Summary
5) Problems of classical transistor
6) Poly-Si emitter
7) Short base transport
8) High frequency response
9) Conclusions
REF: SDF, Chapter 10
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
How to make better Transistor
32
2 2, ,
2 2, ,
1i E i Bn E E n E
B p i B B B i E B s
n nD W N D N
W D n N W n Nβ
υ≈ → ×
Classical Shockley transistor
Heterojunction bipolar transistor
Graded Base transport
Polysilicon Emitter
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Short-base Quasi-ballistic Transistor
33
N+ P
1 2, 2thE n
Bn
nnI qD
Wnq υ−= − = −
1
2 n B
n thB
D W
D W
n
n υ=
+, ,
, ,
n E ballistic
n E s n hi tB
th
D
I
WI
υυ
=+
∆nn1
υth
n2
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Gain in short-base Poly-silicon Transistor
34
, , ,
, , ,
p B poly B poly
p B s p BE
s
ssi iD
I I
I IW
υυ
=+≃
, , , ,,
, , , ,
C ballistic C ballistic C si B sipoly ballistic
B poly C si B si B poly
I I I I
I I I Iβ
= = × ×
, ,
, ,
n E ballistic
n E s
th
thi n B
I
I D W
υυ
=+
Large devices, dinite diffusion length => small diffusion velocity=> thermal velocity is large => neglect diffusion velocity
2,
2,
i Bn E E
n B B p i E
th
th
E s
s
p
B
nD W N
D W W D n N
D W υυυυ
+ ≈ × × +
2,2,
i B E
i E B s
thn N
n N υυ→ × × vs Assume small
vs
Assume smallCompared to diffusion velocity
Quasi-Ballistic transport in very short base limits the gain …
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Outline
35
1) Current gain in BJTs
2) Considerations for base doping
3) Considerations for collector doping
4) Intermediate Summary
5) Problems of classical transistor
6) Poly-Si emitter
7) Short base transport
8) High frequency response
9) Conclusions
REF: SDF, Chapter 10
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Topic Map
36
Equilibrium DC Small signal
Large Signal
Circuits
Diode
Schottky
BJT/HBT
MOS
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Small Signal Response
37
P+
N
P
C
E E
B
VEB(in)
VEC(out)
ICIB
log10 β
log10 f
fT
1
fβ
2
, ,
1
2 2 2B BC B
j BC j BET n sat C
W W k TC C
f D qI
= + + +
π υ
β ω( ) ≈ βDC
ωβ
ω
Desire high fT⇒High IC⇒Low capacitances⇒Low widths
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Frequency Response
38
� The gain of an amplifier is affected by the capacitance associated with its circuit.� This capacitance reduces the gain in both the low and high frequency ranges of
operation.� The reduction of gain in the low frequency band is due to the coupling
and bypass capacitors selected. They are essentially short circuits in themid and high bands.
� The reduction of gain in the high frequency band is due to the internalcapacitance of the amplifying device, e.g., BJT, FET, etc.
� This capacitance is represented by capacitors in the small signal equivalent circuit for these devices. They are essentially open circuits in the low and mid bands.
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Small Signal Response (Common Emitter)From Ebers Moll Model
39
Cµ
( )1 F FIα−
Cπ
IRF F R RI Iα α−
( )/0 1BEqV kT
F FI I e= −
( )11 F F
BE
B B
BE B
Idd q
r dV dV T
I
k
I
π
α =−
= =
( )F C
BE Bm
Fd qI
dV Tg
I
k
α= =
( )F F B BEmm Eg VI gδ δα υ= =
P+
N
P
C
E E
B
VEB(in)
VEC(out)
ICIB
IB
1 C
DC B
qI
k Tβ=
DC Circuit => AC small signal CircuitBC In reverse bias, IR=0
Cµ
Cπrππππ gmVBE
IBIC
IE
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Short Circuit Current Gain
40
( )( )1
1T
T mT
T
m j gf
j C Cj C j
g
Cr
C
π µπ µ
π
µωβ
ω ω ω−
≡ = ≈ +
+ +
( )1
m BE CB
BE BE BCB
Cj
f
j C j
C
Ci
r
gi
π µπ
µω υβ
υ ω υ ω
υ
υ
+= =
+ +
Cπrπ
m BEg υ
Cµ
( ) ( ), , , ,
1 1
2 j BC jT
BBE d B
B
m C CC d BE
T
C k T k T
g
CC C C C
f qI qIπ µ
πω+
≡ = = + + +
,,
d BCB Bd BC
C C BE C
Ck T dQC
qI dI dV dI= =
E
CB
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Base Transit Time
43
B B
C C
dQ Q
dI I=
N+ P
∆n n1
21
1
12
2
BB
n
B
q nW Wn Dq
W
= =
Ref. Charge control model
Base transit time
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Collector Transit Time
44
?BC
sat
W=τυ
N+ P
1
2qi τ× × =
, 2 2BC
eff BCsat
q W
i
ττυ
= = =
t
i τ
Electrons injected into collector depletion region – very high fields more than diffusion => drift => acceleration of carriersCharge imaged in collector
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Putting the Terms Together
45
2
, ,
1
2 2 2B BC
T n sat
Bj BC j BE
C
W W
f D
k TC C
qI
= + +
+
π υ
Base transit time
Collector transit time
Junction charging time
10log Tf
10log CI
Kirk Current
Do you see the motivation to reduce WB and WBC as much as possible? What problem would you face if you push this too far ?
KI
Increasing IC too high reduces WBC and increases the overall capacitance=> frequency rolls off….
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
High Frequency Metrics
46
( ) ( )2
, ,
1
2 2 2B BC B
j BE j BCT n sat C
ex c cb
W W k T qC C R
f DR C
Iτ
π υ= = + + ++ +
(current-gain cutoff frequency, fT)
(power-gain cutoff frequency, fmax)
fmax =fT
8π RbbCcbi
Klimeck – ECE606 Fall 2012 – notes adopted from Alam
Summary
47
We have discussed various modifications of the classical
BJTs and explained why improvement of performance
has become so difficult in recent years.
The small signal analysis illustrates the importance of
reduced junction capacitance, resistances, and transit
times.
Classical homojunctions BJTs can only go so far, further
improvement is possible with heterojunction bipolar
transistors.