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BIPOLARTRANSISTOR
1
Bibliography:
2
• H. Mathieu, « Physique des semi-conducteurs et des composantsélectroniques », 4° édition, Masson 1998.
• D.A. Neamen, « semiconductor physics and devices », McGraw-Hill, Inc 2003.• P. Leturcq et G.Rey, « Physique des composants actifs à semi-conducteurs »,
Dunod Université, 1985.• J. Singh, « semiconductors devices :an introduction », McGraw-Hill, Inc 1994.• Y. Taur et T.H. Ning, « Fundamentals of Modern VLSI devices », Cambridge
University Press, 1998.• K.K. Ng, « complete guide to semiconductor devices », McGraw-Hill, Inc 1995.• D.J. Roulston, « Bipolar semiconductor devices », McGraw-Hill, Inc 1990.
Plan• Geometry• Principle of operating• Static characteristics• Ebers-Moll Equations• Static parameters ( gain…)• Second order effects• Switching performances• Transistor in HF domain• Hetero-junction Bipolar Transistor (HBT or TBH)
3
Geometry
• Geometry:• Lateral• Vertical
• For digital circuits, vertical design
4
lateral
vertical
npn
BC
E
Geometry for IC
5
Muller et Kamins, « device electronics for IC »,2nd Ed., Wiley, 1986
Geometry with insulating oxide
6
Muller et Kamins, « device electronics for IC »,2nd Ed., Wiley, 1986
BJT always present: why?• speed• Low noise• High gain• Low output resistance
• Still present in mobile phone ( analog part)• Low density, mainly in power stage• BiCMOS
7
Analogueamplifier
Working principle
• 2 PN Junctions with one common region (base)• The first Junction (EB) will
inject carriers• The second one (CB) will
collect carriers• The base must be thin (lower than diffusion length)
8
• Reverse biased Junction:• Low current due to empty
tank , reservoir.• By modifying the filling of the
tank, we can modulate the collected current (collector)
• We fill the reservoir ( the base) par a forward bias of the EB junction.
9
Working principle
• The reverve biasing CB junctioncreates a favorable electric fieldfor the collect
• Conditions: • Thin base:
• Avoid recombination effects• Ligthly doped base compared to
emitter• favors one type of injected
carriers (better injection efficiency)
10
Working principle
Statics characteristics
11
NPN Transistor NPN Transistor
12
Minority carrier distribution in a forward biased npntransistor
ideal
With recombination
13
PNP Transistor
No recombination in the Base ! ( )
1D Approximation
Homogeneous doping in the Base
Low Injection
Statics characteristics + simplifying hypotheses
Current components in the NPN Transistor• In the neutral Base region:
• Fundamental equation
• and ,
• Integrating from E-B to C-B:
• finally:
• In forward active regime, Jn is negative ( e- vers x<0)
14
dxnpd
eDJ
neDJ
pp
p
n
n ).(
dxnpd
eDJ
neDJ
pp
p
n
n ).(
pn JJ pn
dxnpd
eDJ
pn
n ).(
dxnpd
eDJ
pn
n ).(
'
'
)(
)exp()exp(2
C
E
BCBE
iBnbn
dxxp
kTeV
kTeV
neDJ
'
'
)(
)exp()exp(2
C
E
BCBE
iBnbn
dxxp
kTeV
kTeV
neDJ
'
'
)(
)1()1(2
C
E
kTeV
kTeV
iBnbn
dxxp
eeneDJ
BCBE
'
'
)(
)1()1(2
C
E
kTeV
kTeV
iBnbn
dxxp
eeneDJ
BCBE( )( )
( )( )
P P
N N
dp xJ eD p x
kT dxdn x
J eD n xkT dx
15
)1(
)()1(
)()(
)1()1(
'
'
'
'
'
'
222 kT
eV
C
E
iBnbkTeV
C
E
iBnbC
E
kTeV
kTeV
iBnbn
BCBE
BCBE
edxxp
neDedxxp
neD
dxxp
eeneDJ
)1(
)()1(
)()(
)1()1(
'
'
'
'
'
'
222 kT
eV
C
E
iBnbkTeV
C
E
iBnbC
E
kTeV
kTeV
iBnbn
BCBE
BCBE
edxxp
neDedxxp
neD
dxxp
eeneDJ
and:BeffA
C
E
WNdxxpB
'
'
)( BeffA
C
E
WNdxxpB
'
'
)(
So:
)1()1()1()1(
22kT
eVkT
eV
SnkT
eV
BeffA
nbiBkTeV
BeffA
nbiBEn
BCBEBC
B
BE
B
eeIeWNDene
WNDenAI
)1()1()1()1(
22kT
eVkT
eV
SnkT
eV
BeffA
nbiBkTeV
BeffA
nbiBEn
BCBEBC
B
BE
B
eeIeWNDene
WNDenAI
with :B
iE
BeffA
nbiBESn G
enAWNDenAI
B
22
B
iE
BeffA
nbiBESn G
enAWNDenAI
B
22
Saturation current of electrons in the PN narrowjunction ( or without recombination in the Base).
BeffnbiB
iBeff
nb
A
iB
iB W
Dp
nnW
DN
nnG B
2
2
2
2
BeffnbiB
iBeff
nb
A
iB
iB W
Dp
nnW
DN
nnG B
2
2
2
2
Gummel number in the Base (s/cm4)
Current components in the NPN Transistor
in the case of uniform base doping
• Emitter current • Collector current
16
1)exp(
kTeVJJ BE
spEpE
1)exp(
kTeVJJ BC
spCpC
finally
pCpEECB
npCC
npEE
IIIII
III
III
E B C
JpE Jn JpCIE
IB
IC
NPN
Current components in the NPN Transistor
• And :
17
)1(exp)1](exp[ kT
eVIkT
eVIIIII BCsn
BEspEsnpEnE
)1](exp[)1(exp kT
eVIIkT
eVIIII BCspCsn
BEsnpCnC
1)exp(1)exp(
kTeVI
kTeVIIIIII BC
spCBE
spEpCpECEB
Current components in the NPN Transistor
• Forward active region:• E‐B (forward) and C‐B (reverse)
18
kTeVII
kTeVI
QQDnAeI BE
SpESnBE
SpESB
nBiE exp)(exp)(
22
2 2
( )exp expi nB BE BEC Sn
B S
Ae n D eV eVI I
Q Q kT kT
kTeVIIII BE
SpECEB exp*
Statics characteristics
• Emitter injection efficiency:
• DC common base current gain:
• DC common emitter current gain :
19
exp( / )exp( / )
Sn BE SnnE
pE SpE BE Sp
I eV kT III I eV kT I
1 to close but 1).(
1
1
22
SpSn
Sn
nBi
SBSpE
C
III
DneQQJI
I
ESp
Sn
B
C
II
II
1
NB:if we neglect recombinationprocess and are equivalent E
Statics characteristics
• Base transport factor:• Take into account recombination
in neutral base region
20
( (0) ) / 2effB p ps
rBn n
AeW n nQI
t
sC
QI
2
2
21
eff
C n n
rB t B
I LI W
Statics characteristics
• Recombination factor:• Take into account recombination in
depleted base region
21
exp2 2
i BErD T
Aen eVI W
kT
withWT, width of E‐B space charges.
When we add up all the contribution to the base currentwe get:
rDrBBB IIII *
Statics characteristics
• The common emitter gain can be expressed as:
22
C
rD
EC
rDrBB
C
B
II
IIII
II
111 *
Statics characteristics
2 5
2 8
2 101000
10eff
n
B
LW
2
2 1000E E
B B
D DEeffSn iB nBE
SpE iE pE A Beff A
N NWI n DI n D N W N
2
5
80
expexp 2 10exp exp
2 10 2exp exp
2 2 2
B
B
i nB BEBE
Sn A BeffC i nB BE BE
rD A Beff TBE i BEGR T
Aen D eVeVI N W kTI nD eV eVkTI N W W kT kTeV Aen eVI W
kT kT
• IB intrisic base current (no recombination)
• IrB recombination current in the neutral base region
• IrD recombination current in the depletionzone of EB junction
If VBE>0,72V then exp() larger than 106
Modern Transistors:
Other modes of operation
• Saturation mode (regime):• The two junctions are forward biased.
23
kTeV
BS
nBikTeV
spEBS
nBiE
BCBE
eQQDnAe
eIQQDnAe
I
2222
kTeV
spCBS
nBikTeV
BS
nBiC
BCBE
eIQQDnAee
QQDnAeI
2222
QS1
nex(0)
WB
QS2
nex(W)
WB
nex(0)nex(W)
QS1+QS2
WB
• Low injection : (QS<<QB):• Current is due to saturation charge injected into the base, ie
QST = QS1 +QS2
• If we deal with « narrow » junction, this charge is simplygiven by the surface of ½ trapeze (linear decay)
24
kTeV
sntkT
eV
A
iBBBS
kTeV
sntkT
eV
A
iBBS
BCBC
BEBE
eJeNnWWxenWQ
eJeNnWxenWQ
2
2
2
1
21)(
21
21)0(
21
Saturation mode
Saturation mode
• Low injection: (QS<<QB):• An other « view » of saturation charge (from Ablard):
• We consider transistor in active mode with a charge QSN and a charge QSAT (we have to determine) which supply the samesaturation current Icsat.
25
0 WB
n(x)
)0(exn
)( Bex Wn
Base
)()0( Bexex Wnn
QSN
QSAT
kTeV
sntkT
eV
sntSN
BBSN
BCBE
eJeJQ
WWnneQ
))()0((21
kTeV
sntkT
eV
sntSN
BBSN
BCBE
eJeJQ
WWnneQ
))()0((21
We get :
kTeV
sntSAT
BC
eJQ 2 kTeV
sntSAT
BC
eJQ 2
Responsible for the degradation of dynamic performance
QST = QSN+QSAT
Nonideal Effects
• « Gummel plot »:• Graph of IC and IB versusVBE
26
1
2
3
• Early effect / collector punchthrough
• Base – collector junction breakdown
• Emitter and Base serie resistance
• Ic « collapse » fort high current
• « crowding effect »
• Early effect / collector punchthrough
• Base – collector junction breakdown
• Emitter and Base serie resistance
• Ic « collapse » fort high current
• « crowding effect »
27
Nonideal Effects
• At "first glance" Ic is independent of VCB
• In fact we have the modulation of the width of the neutral region in the base, so in the same wayQB+QS , and so Ic !
28
'
'
2 2 2 2 2 2
( )exp exp exp
( ) B
i nB BE i nB BE i nB BEC C
B S A Beff
E
Ae n D eV Ae n D eV Ae n D eVI
Q Q kT kT N W kTp x dx
if VBC WB QB+QS
Ic
ZCE B-C
Early effect / collector punchthrough
29
BCZCE
SC
BB
dBC
pBA
W
WeNCQ
V
Early effect / base punchthrough
Collector current is due to diffusion of electrons in the base
• At the limit:• The space charge BC
« depletes » totaly the neutral base
• collector injects directlycurrent into the emitterbecause energy barrier islowering
• Current only limited by serieresistance Rserie from E and C
30
C
CBB
DSC
DAABpt N
NNNeWV
2)(2
Early effect / base punchthrough
Base - Collector junction breakdown
• Avalanche of BC:• Often occurs before punchthrough
• How to prevent it?• Lowering the electric field:
• Reduce the doping gradient in the collector
• Lightly doped layer between base and collector
31
Ionisation par impacts
BrBfB III BrBfB III
Emitter and Base resistance (effet 3)
• At low current negligeableeffects
• In high speed circuits, B-C allways reverse biased (rc2 and rc3 as low as possible)• Resistances rc have no
effects on current flow• Only re and rb play a major role .
• IR drop Voltage
32
)exp(
)(
'
'
kTVeII
VVV
rrIIrrIIrV
BEBB
BEBEBE
beBCebBEeBE
0 BEC III
Measured current:IB’
Collector « collapse » for high injection level (effect 1)
• Numbers of physicalmechanisms can cause thisfalloff of IC0:• Increase of the charge (holes)
into the base (maintainneutrality)
• Increase the width of the quasineutral base layer (push off the space charge into the collector): Kirk effect
33
kTeV
dxxpneDAI
kTeVJAI
BEC
E p
ieBnBEC
BECEC
exp)(
exp
'
'
2
0
Nc
Nb
x)
Wb0
E’ C’
Nc-n
Nb+n
x)
Wb0
E’ C’
34
And the effect #2 ????????????????
« crowding effect »
• The view of a 1D devices is an approximation
• Drop voltage IR in the base. • The edge of the emitter contact is
more biased than the core/center• Favour a high density of current
essentially along the edges• Not a good thing for high power
devices
• Solutions: interdigitatedapproach
35
Bipolar Transistor: a switch ?
• ON state: the switch isclosed (saturation mode)
• OFF state: the switch is open (cutoff mode)
• ON state: the switch isclosed (saturation mode)
• OFF state: the switch is open (cutoff mode)
36
• Input signal as low as possible
• input power as low as possible
common emitter
• Input signal as low as possible
• input power as low as possible
common emitter
37
Bipolar Transistor: a switch ?
• Switching velocity?• Limiting factors?
38
Turn on transient: Continuity equation
for the charge:
B BB
n
Q dQI
dt
Base charge can bewritten:
Collector current is givenby:
transit time
in the base (narrow)
( ) [1 exp( )]B B nn
tQ t I
( )( ) B
Ct
Q tI t
( )[1 exp( )]B n
c Bt t n
Q t tI I
Bipolar Transistor: a switch ?
• Turn on:• IC increases until the saturation
regime is reached:(we neglect VCEsat)
• The limit charge QB(ton) to saturate the transistor is givenby :
• The on state time is given by:
39
C
DDC R
VIsat
C
DDC R
VIsat
nB
pBCS D
dIQ sat
2
2
nB
pBCS D
dIQ sat
2
2
)(1
1ln)(1
1ln
Bc
nnBS
nON IIIQt
)(1
1ln)(1
1ln
Bc
nnBS
nON IIIQt
)]exp(1[)(n
nBBtItQ
Bipolar Transistor: a switch ?
• Remark: the charge can increaseover QB(ON) to over saturate the transistor.this charge is injectedfrom the collector
• Turn off time : input with a « 0 »:• Evacuation of the stored charge
• This is the storage time ts
• after, this is the samemechanism than for PN Junction
40
S
nBnS Q
It
ln
S
nBnS Q
It
ln
Final value:
Bn I
Bipolar Transistor: a switch ?
• Storage time (desaturation) limits the switching time
• 2 ways to reduce it:• Add impurities which
decrease strongly the lifetimeinto the base (pb withtransport factor)
• Schottky Diode in // with CB junction: avoid saturation of the transistor
41
Bipolar Transistor: a switch ?
AC signal : equivalent circuitAC signal : equivalent circuit
42
CµIB Ib Ic
Transistor and ac signal: equivalent circuit
• Transconductance :links the variation of the collector current to the base – emiter voltage:
• Input resistance : links the variation of Base current to the base – emitervoltage:
• Output resistance:
43
.C Cm c m BE
BE
I eIg i g v
V kT
1
11B
BE B m
I kTr h
V eI g
1
22
1C Ao
CE C
I Vr
V I h
• Capacitance :
• Storage capacitance
• transit time
• Capacitance : CB junction capacitance reverse biased
• Collector –substrate (depletion layer) capacitance:
44
EBTSE CCC
CBTCC
dCSC
mFSE gC
BCBEB tttEF tttt
C
C
Transistor and ac signal: equivalent circuit
• Cut off frequency (current gain =1 when short circuit load)• We neglect r0
• Current gain is given by:
45
beµb
beµbemc
vCjCjr
i
vCjvgi
1
21)()/1()( h
CCjrCjg
ii
µ
µm
b
c
21)()/1()( h
CCjrCjg
ii
µ
µm
b
c
Transistor and ac signal: equivalent circuit
21 00 then (0) static gain(1 / )
c mm
b
i gif g r h
i r
21 00 then (0) static gain(1 / )
c mm
b
i gif g r h
i r
• In modern devices , in general• At low frequency:
• At high frequency, the imaginary term dominates and :
46
mµ gC
)(1)(
µ
m
b
c
CCrjrg
ii
)(1)(
µ
m
b
c
CCrjrg
ii
)()(
µ
m
CCjg
)(
)(µ
m
CCjg
Transistor and ac signal: equivalent circuit
Transistor en ac: schéma équivalent
• We get the « cutoff frequency » by considering iC/iB=1
• By replacing all the terms by their expressions
47
µ
mT CC
gf
2
)()(2
1ceTTSE
CF
T
rrCCCeIkT
f BCBC
Forward Transit time
12 ( )
m
T µ
gf C C
12 ( )
m
T µ
gf C C
Resistance neglected
Transistor en ac: schéma équivalent
• Maximun oscillation frequencyPower gain=1• Laborious and tedious calculation/ we have to take into account the
base resistance
48
dBCb
T
Crff
8max dBCb
T
Crff
8max
Heterojunction Bipolar Transistor
• Current gain:
• In the case of narrow base:
49
2 2
2 21 12
E E B
E B B E B
i p A Beff Beff
D n i p n
n D N W WN D n L L
2 2
2 21 12
E E B
E B B E B
i p A Beff Beff
D n i p n
n D N W WN D n L L
2
21 E E B
E B B E
i p A Beff
D n i p
n D N WN D n L
2
21 E E B
E B B E
i p A Beff
D n i p
n D N WN D n L
• If we want a gain with a high value, we need close to 1. It means: • Lowering base doping• Lowering base width (careful with punchthrough!)
50
Increase of the base resistance fmax decreases
2
21 E E B
E B B E
i p A Beff
D n i p
n D N WN D n L
2
21 E E B
E B B E
i p A Beff
D n i p
n D N WN D n L
Heterojunction Bipolar Transistor
• Other solution:• Increase emitter doping
• Improve emitter efficiency• Problem: « gap shrinking »
• This « problem » can be transform in opportunity !! (next twoslides)
51
2
21 E E B
E B B E
i p A Beff
D n i p
n D N WN D n L
2
21 E E B
E B B E
i p A Beff
D n i p
n D N WN D n L
)exp()()( 22
kTE
Basenémetteurn gii
.0)()( émetteurgbasegg EEE
Heterojunction Bipolar Transistor
52
kTE
LW
nN
DD
Nn g
p
Beff
i
A
n
p
D
i
EB
B
B
E
E
e exp1 2
2
kTE
LW
nN
DD
Nn g
p
Beff
i
A
n
p
D
i
EB
B
B
E
E
e exp1 2
2
1)exp(
1 kTE
WL
DD
NN g
Beff
p
p
n
A
D E
E
B
B
E
1)exp(
1 kTE
WL
DD
NN g
Beff
p
p
n
A
D E
E
B
B
E
We see that it is difficult to have at the same time a large emitter doping, a lightly doped and thin base and a large gain
Heterojunction Bipolar Transistor
• We design a structure with a negative energy gap difference: this is an HBT
53
eb EgEgEg
Heterojunction Bipolar Transistor
54
Requirements for a bipolar device
•High gain
•High emitter efficiency
•High speed
Demands and Problems for a BJT
Demands Problems
Heavy emitter doping Bandgap shrinkage causingbase injection
Low base dopingNarrow base width High base resistance
Solution: Heterojunction Bipolar Transistors
•Emitter can be heavely doped using a SC with Eg larger than the base semiconductor•Base can be heavely doped and be made narrow without increasing base resistance•Collector can be chosen from a material to increase breakdown voltage
(From Singh)
55
Transistor with a Silicon –Germanium base
56
Electrons density
kTeV
IQQDnAe
I BESpE
SB
nBiE exp)(
22
kTeV
QQDnAeI BE
SB
nBiC exp)(
22
emettir collector
base
)(2 Sini
)(2 SiGeni
Improve gainImprove transist timeIncrease Early voltage