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22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #1
Bipolar Junction Transistors
• Bipolar junction transistors (BJT) are active 3-terminal deviceswith areas of applications:– amplifiers, switch etc.– high-power circuits– high-speed logic circuits for high-speed computers.
• BJT structure:– sandwich of alternating type of Si-layers
♦ npn BJT: sequence of n-p-n♦ pnp BJT: sequence of p-n-p
– npn BJTs are most widely used.
N+ P
E B C
N- N+
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #2
A. IC BJT Structure
a) 2d-cross-section of an npnBJT structure.
1.E+15
1.E+16
1.E+17
1.E+18
1.E+19
1.E+20
1.E+21
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Depth (um)
Co
nce
ntr
atio
n (c
m-3
)
N+ Emitter
P Base
N- Collector
N+ Burried layerN+
P−
N-EpiP+ P+N+P N+
Contacts
Active region
NPN
b) 1d-cross-section alongthe intrinsic device.
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #3
B. Basic Features of IC BJT Structures
• The base region is non-uniformly doped. This results in a built-inε field across the base which aids the transport of e− from E → C.
• Parasitic elements exist in a BJT structure such as:– base resistance, RB from base contact to active area– collector resistance, RC (predominantly through n- layer).
• Isolation must be provided between adjacent devices:– reverse biased PN junctions– trench isolation.
• The N- collector region adjacent to the base:– reduces CBC, improves BVCB
– decreases base width modulation by the collector voltage– but adds series resistance to the device.
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #4
C. Basic BJT Operation
• The BJT operation is as follows:– An external voltage is applied across the E-B junction to forward
bias it (≈ 0.7 V)
– e− are injected into the base by the emitter. (Also, holes areinjected into the emitter but their numbers are much smallerbecause of the relative values of NA, ND).
B
E C
≈ 0.7 Vforward bias
XB
e− Mostof the
e−
N+ P N- N+
− + − +
5 Vreverse bias
hole
s
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #5
Basic Operation
– If XB << LN (diffusion length) in the base, most of the injected e-get into the collector without recombining. A few do recombine;the holes necessary for this are supplied as base current.
– The e− reaching the collector are collected across the C-B junctiondepletion region.
Since most of the injected e- reach the collector and only a few holesare injected into the emitter, the required IB << IC.
Therefore, the device has a substantial current gain.
ICIEElectrons flowingemitter to collector
Recombining electronsHoles
into emitter
E B C
IB
ICIB
IE
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #6
Basic Operation - Derivation of Currents
In order to derive the basic relationship for e- current flowingbetween E and C, we assume that the device current gain is high.
∴ IB ≅ 0
∴ Jp ≅ hole current in base = 0
∴ Jp ≅ 0 = qµppεx − qDp(dp/dx) (1)
For uniformly doped base, εx = 0 and the e- travelling through thebase will move by diffusion only.
However, in IC transistors dp/dx ≠ 0 and εx ≠ 0. The direction ofthis field aids e- flow from E → C and retards e- flow from C → E.
dxdp
pqkT
dxdp
pD
p
px
11==
µε (2)
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #7
Basic Operation - Derivation of Currents
The e- flow between E and C is given by:
Jn = qµnnεx + qDn(dn/dx) (3)
Using (2) in (3) we get:
We integrate (5) over the quasi-neutral base region of width xB.
+=∴
dxdn
pdxdp
npDq
J nn
dxdn
Dqdxdp
pn
kTJ nnn += µ (4)
( )dxpnd
pDq
J nn = (5)Or,
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #8
Basic Operation - Derivation of Currents
Jn is pulled outside the ∫ assuming no recombination of e- in thebase region, i.e. Jn = constant.
BE C
xB
N+ P N-xd2xd1
x = 0 x = xB
dxx
dxpnd
D
dxx
qp
JBB
ono
n ∫∫
=∴ (6)
( ) ( )0pnxpnD
dxx
qp
J Bno
n
B
−=∴ ∫ (7)
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #9
From PN junction analysis, the pn-products at the edge of thedepletion regions are:
Now, the total charge in the un-depleted base region is given by:
Basic Operation - Derivation of Currents
( )( )
∫
−
=∴
=
=
x
Dpdx
eenqJ
enxpn
enpn
B
o n
kTV BEq
kTV CBq
i
n
kTV CBq
iB
kTV BEq
i
2
2
20 (8)
(9)
(10)
∫=x
pdxqAQB
oB (11)
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #10
This is an extremely important result. Note that:1 Usually, only one of the two exponential terms is important since
one junction is typically reverse biased. When the device is insaturation, both junctions are forward biased and both terms mustbe included.
2 The quantity, is called the base Gummel number.
It is the total integrated base charge (atoms/cm2). Since I ∝ 1/QB, itis important to minimize QB. Therefore, IC transistors use low basedoping levels.
Basic Operation - Base Gummel Number
−=∴ eeII kT
V BEqkTV CBq
sn (12)
(13)Q
DnAqI
B
nis
222
and, =
∫=x
dxxNqAQ B
o
AB )(
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #11
Since BC junction is reversed biased the eqVBC/kT term is negligibleand we can show from (12) and (13):
IC Vs. VBE
(14) predicts that IC vs. VBE is relatedexponentially. Slope = (kT/q)ln(10)
= 60 mV/decade I (@ 25 oC)
Relationship holds extremely well for ICtransistors over many decades of current.
Generally, QB is obtained by integrationover the base region. Therefore, QB istypically well controlled to ~ 1012 cm-2 togive high IC for a given VBE.
−−=∴ 1
222
eQ
nDAqI kT
V BEq
B
inn (14)
1.E-10
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
0.0 0.2 0.4 0.6
VBE (V)
J C (
A/c
m2 )
Expt
Ideal
Decadechangein JC
60mVJS
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #12
D. Current gain
• Let us consider the factors that can contribute to base current in aBJT:– Recombination in the neutral base region– Hole injection into the emitter– Recombination in the E-B space charge region
ICIEElectrons flowingemitter to collector
Recombining electronsHoles
into emitter
E B C
IB
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #13
1. Recombination in the Neutral Base Region
Typically, some of the e- traveling the base will recombine withmajority carrier holes. (This is not important for modern IC BJTs).
If we assume that the base is uniformly doped so that εx = 0, the e-current and continuity equations are:
N+ Nnp
npo
P
QBpn
pno
pno
02
2
=−
−
=
τ n
ppn
pnn
n pn
xdnd
D
dxnd
DqAI
o
(15)
(16)
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #14
Recombination in the Neutral Base Region
As we discussed for PN junction, the general solution of theseequations is:
np − npo = K1e−x/Ln + K2ex/Ln (17)
The appropriate boundary conditions are:
np(x = 0) = npoeqVBE/kT
np(x = xB) ≅ 0
Using these boundary conditions we get from (18):
Substituting (18) into (15) we get emitter and collector e− currents.
−
=
LxL
xx
eV
nn
n
B
n
B
kT
q
ppBE
o
sinh
sinh(18)
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #15
Base Transport Factor
The ratio of these two currents is defined as the base transportfactor and is given by:
αT ≡ InC/ InE
= sech(xB/Ln) (21)
In modern IC BJTs, XB << Ln and recombination in the neutralbase region is significantly low.
If XB << Ln, (19) reduces to our earlier expression for e- current(14) and the base transport factor αT becomes:
αT ≅ 1 − xB2/2Ln
2
−=
−=
Lxhe
V
L
n pDqAIn
Lx
eV
L
n pDqAIn
n
BkT
q
n
n
C
n
BkT
q
n
n
E
BEo
BEo
csc1
coth1 (19)
(20)
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #16
In a typical advanced BJT, XB ≤ 1 µm and Ln ≥ 30 µm ∴αT ≅ 0.9994.
This value of αT would imply a forward current gain:
which is higher than normally observed value of βF in IC BJTswith 1 µm base widths. Thus, αT is NOT usually a limiting factor incurrent gain.
The base current due to αT is:
where τn is e− lifetime in the base.
−= 1
2
2
eN
xnAqI kT
V BEq
nA
BiEBREC τ
(22)
Base Transport Factor
16001
>−
=−
≅≡T
T
nCnE
nET
B
CF II
III
ααα
β
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #17
The dominant mechanism in limiting β in modern BJTs is hole injection intothe E from B. Note that this process must occur because VBE decreases thebarrier to e- flow from E → B and also the barrier for hole flow from B → E.
The injected hole currents in each case come directly from the analysis of longbase and short base diodes (E denotes emitter properties):
2. Hole Injection into the Emitter
−=<<
−=>>
1:
1:
2
2
eV
xND
nqAILx
eV
LND
nqAILx
kT
q
EDE
pEipEpEE
kT
q
pEDE
pEipEpEE
BE
BE
(23)
(24)
E B CxE xB
nppn pn
xE >> LpE
xE
xE << LpE
E B C
nppn pn
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #18
The injection efficiency of the emitter is defined as:
Then from (14) and (24) we get:
(If XB >> Ln or XE >> Lp, then LB diode approximations replace XBand/or XE with Ln or Lp.)
(26) is only approximately correct in IC structures because NA andND are not constant. Note that γ is made close to 1 by: (1) making NDE >> NAB; (2) XB small; (3) XE large (prevent hole recombination at E contact).
Emitter Efficiency
III
III
I
nE
pETOT
nE
pEnE
nE
+==
+=
1
1γ (25)
DNDN
xx
nBDE
pEAB
E
B+=
1
1γ (26)
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #19
3. E-B Space Charge Recombination
αT and γ are independent of VBE imply that the ratio of collector tobase current is a constant, independent of VBE i.e. current level.
In practice, the ratio of the two currents is NOT independent of IC.At low levels the dominant reason is recombination in the E-Bdepletion region.
From PN junction theory, we find that some recombination of thecarriers moving through the depletion region will occur, causing arecombination current.
E B Ce−
injection
holeinjection
*recombination
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #20
E-B Space Charge Recombination
where τo is the lifetime in the depletion region.
Note:– This current flows in the EB circuit and does not directly affect IC.
Thus, as IREC becomes important, the ratio of IC/IB will change.
– eqVBE/2kT dependence is important at low current levels.
Summarizing our discussion of current gain:
eWnqA
I kTVq
o
EiREC
A
22τ
= (27)
II
III
II
II
nE
REC
nE
nCnE
nE
pE
C
B +−
+≅≡β1
eV
nDWxN
Lx
DxNDxN
kT
q
oin
EBA
n
B
nED
PBA BE
22
2
221 −++≅
τβ(28)
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #21
E. Mode of Operations
BJTs are two back-to-backdiodes.N+ P
E B C
N- N+E C
B
BE C
Four modes ofBJT operations
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #22
Mode of Operations
1) Forward active / normal– BE junction forward biased– BC junction reversed biased
here,,BFC
BC
IIII
β=∴∝
where βF = forward gain
2) Reverse active– BE junction reverse biased and BC junction forward biased
here, reverse gain, βF = IE/IB ≈ 1
3) Saturation region– BE and BC are forward biased
4) Cut-off region– BE and BC are reversed biased
+ VBC
+ VBE
−
−
Saturation
NormalCut-off
Inverse
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #23
F. Basic BJT Model
Basic BJT model can be derived considering two back-to-backdiodes as npn-BJT.
1) B-E junction is forward bias:– forward current, IF flows through E-B diode.
− αFIF flows in the collector
here, αF = forward gain ≅ IC/IE if VBE is +ve
2) B-C junction is reverse bias:– reverse current, IR flows through B-C diode.
− αRIR flows in the emitter
here, αR = reverse gain ≅ IE/IC if VBE is +ve
n p
E B C
n
E C
IE IC
B IB
IF αFIF
aRIR IR
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #24
EM1 BJT Model: Injection Version
• The basic Ebers-Moll model (EM1):
E OIE
O CIC
IB
αRIR αFIF
OB
IF IR
• Terminal currents: IE = − IF + αRIR (29)
IC = αFIF − IR (30)
IB = IF − αRIR − αFIF + IR
= (1 − αF) IF + (1 − αR) IR
∴ IB = (1 − αF) IF + (1 − αR) IR (31)
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #25
EM1 BJT Model: Injection Version
• We know from current flow analysis:
Here IES = E-B saturation current; VBE = B-E voltage ICS = C-B saturation current; VBC = B-C voltage
• The terminal currents from (29), (30), (32), (33):
−==
−==
1
1
eIII
eIII
kTV BCq
CSnCR
kTV BEq
ESnEF (32)
(33)
−−
−=
−+
−−=
11
11
eIeII
eIeII
kTV BCq
CSkTV BEq
ESFC
kTV BCq
CSRkTV BEq
ESE
α
α (34)
(35)
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #26
EM1 BJT Model: Injection Version
• From reciprocity property: αFIES = αRICS ≡ IS
• Therefore,
• Again, βF = CE forward current gain = αF/(1 − αF) βR = CE reverse current gain = αR/(1 − αR)
• Since IS = f(ni2) = f(T)
−−
−=
−+
−−=
11
11
eI
eII
eIeI
I
kTV BCq
R
SkT
V BEq
SC
kTV BCq
SkTV BEq
F
SE
α
α(36)
(37)
−−
=∴ ref
g
TTkE
refrefSS e
TT
TITI113
)()( (38)
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #27
EM1 BJT Model: Injection Version
• Model equations:
Where αF = βF/(1 + βF) αR = βR/(1 + βR)
∴ Total five model parameters: βF, βR, IS, Tref, and Eg can be used todescribe basic BJT device characteristics without parasitics.
−−
−=
−+
−−=
1)(
1)(
1)(1)(
eTI
eTII
eTIeTI
I
kTV BCq
R
SkT
V BEq
SC
kTV BCq
SkTV BEq
F
SE
α
α(36b)
(37b)
−−
= ref
g
TTkE
refrefSS e
TT
TITI113
)()( (38)
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #28
EM1 BJT Model: Transport Version
Model equations (36) and (37) can be written as:
Where the reference source currents:
ECR
CCC
ECCCF
E
III
III
−+=
+
−=
α
α
1
1(39)
(40)
−=
−=
1
1
eII
eII
kTV BCq
SEC
kTV BEq
SCC
E OIE
O CIC
IB
IEC ICC
OB
ICC/αF IEC/αR
ECR
CCF
B III
−+
−=∴ 1
11
1αα
(41)
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #29
EM1 BJT Model: Nonlinear Hybrid-π
• From transform model (39) and (40), we get:
• Where the reference source current is:
• The diode currents are:
( )
( )R
ECCTEC
RECCCC
CTF
CCECCCCC
FE
IIIIII
II
IIII
βα
βα
−=
−−−=
−−=−−
−=
11
11 (42)
(43)
−−
−=−= 11 eeIIII kT
V BCqkT
V BEq
SECCCCT (44)
−=
−=
1
1
eII
eII
kTV BCq
R
S
R
EC
kTV BEq
F
S
F
CC
ββ
ββ(45)
(46)
22-Jan-04 HO #6: ELEN 251 - Bipolar Transistors Saha #30
EM1 BJT Model: Nonlinear Hybrid-π
• The model:
• The terminal currents:
E OIE
O CIC
IB
ICT = ICC - IEC
OB
ICC/βF IEC/βR
+
=
−=
−
−=
R
EC
F
CCB
R
ECCTC
CTF
CCE
III
III
II
I
ββ
β
β(47)
(48)
(49)