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Solid State Electronic Devices (Prof. Edward Yi Chang) p 1
Chapter 5 Bipolar Transistors
1. Higher current and high voltage capability → Power application
2. Faster switching times (fastest transistors ever reported ft > 800 GHz)
Basic Structure
Some facets about bipolar devices
1. The base region is non-uniformly doped, this results in a built- in ε field across the
base which aids the transport of e- from emitter to collector.
2. Parasitic exist in the structure
RB: base resistance from base contact to active base area
RC: collector resistance (predominately through N- layer)
3. The N- collector adjacent to the base reduces CBC, improves BVCB decreases base
width modulation by the collector voltage but adds series resistance to the device.
Basic operation
1. An external voltage is applied across the E-B junction to forward bias it. (≒0.7 V)
2. e- are injected into the base by the emitter
(Holes are also injected into the emitter by the base, but their numbers are much
smaller because relative number of NA, ND)
3. If WB << Ln in the base, most the injected e- get to the collector without combining
a few do recombine, the holes necessary for this are supplied as base current.
4. The e- reaching the collector are collected across the C-B depletion region.
Solid State Electronic Devices (Prof. Edward Yi Chang) p 2
Since most of the injected e- reach the collector and only a few holes are injected into
the emitter, i.e. IB<<IC.
The device has substantial current gain
1B
C
I
I
Internally, the control parameter is VBE (determines the injection level)
Bipolar is considered a current controlled device with IB provided externally
producing IC.
To derive the basic relationship for e- current between E & C, we start by assuming
the device current gain is high ∴ IB=0
diffusion
p
drift
xpp
p
dx
dpqDpqJ
J
0
0base in thecurrent hole
ip)relationsh(Einstein 1
1
dx
dp
pq
kT
dx
dp
p
D
dx
dpDp
p
p
x
pxp
Thus, for uniform doping in the base εx=0 and e- travelling through the base will move
by diffusion only.
In IC transistors, 0 and 0 dx
dpx
The direction of this field aids e- flow E→C and retarded flow C→E.
The e- flow between E & C is given by
diffusion
n
drift
n
nxnn
dx
dnqD
dx
dp
p
nkT
dx
dnqDnqJ
Solid State Electronic Devices (Prof. Edward Yi Chang) p 3
dx
dnp
dx
dpn
p
qDJ n
n
or
dx
pnd
p
qDJ n
n
)(
Neglecting depletion regions, the effective base width XB = metallurgical base width.
BB XX
n
n dxdx
pnd
D
dx
q
pJ
00
)(
Assume no recombination of e- in the base, i.e. constantnJ
)0()(0
pnXpnD
dx
q
pJ B
X
n
n
B
From our diode analysis, we know that the pn product at the edge of the depletion
regions are given by
kT
qV
po
po
enn
pp
kT
qV
iB
kT
qV
i
CB
BE
enXpn
enpn
2
2
)(
)0(
B
BECB
X
n
kT
qV
kT
qV
in
D
pdx
eeqnJ
0
2 )(
Solid State Electronic Devices (Prof. Edward Yi Chang) p 4
region base undepletedin charge total0
BX
BQpdxqA
)( kT
qV
kT
qV
Sn
BECB
eeII
Where
B
niS
Q
DnAqI
222
This is an extremely important result
1. Usually one of two exponential term is important because of the fact that one
junction is typically reverse biased. (If both are forward biased both term must be
included → saturation)
2. The quantity BX
AB dxxN
qA
Q
0
)( is called the base Gummel Number.
It is the total integrated base charge (atoms/cm2)
Since BQ
I1
It is important to minimize QB; IC transistors use low doping levels in the base.
If the base is uniformly doped, 0x
pn np because of relative doping
If the base doping level is constant (NA), then
BAB XqANQ
And we have
1
2
kT
qV
BA
inn
BE
eXN
AnqDI
D
ino
kT
qV
non
A
ipo
kT
qV
pop
N
np
epp
N
nn
enn
BE
BE
2
2
Solid State Electronic Devices (Prof. Edward Yi Chang) p 5
kT
qV
kT
qV
Sn
BECB
eeII
Where
B
niS
Q
DnAqI
222
biased) reverse isjunction BC thebecause negligible is term (The kT
qVCB
e
Alternatively, this may be written as
1
222
kT
qV
B
inn
BE
eQ
nDAqI
This equation predicts an exponential relationship between IC and VBE.
Relationship holds well for IC transistor over many decades of current.
In general, QB is obtained by integration over the base region, QB is well controlled to
1012/cm2 to give high IC for a given VBE.
Current Gain
B
C
I
I
A number of factors can contribute to the current in a BJT (bipolar transistor)
Solid State Electronic Devices (Prof. Edward Yi Chang) p 6
AA.. RReeccoommbbiinnaattiioonn iinn tthhee nneeuuttrraall bbaassee rreeggiioonn
In the general case, some of the e- traversing the base will recombine with majority
carrier hole. (This is usually unimportant)
If we assume the base is uniformly doped, 0x , the the e- current (transport) and
continuity equations are
02
2
n
popp
n
p
nn
nn
dx
dndD
dx
dnqADI
The general solution of the equation is
nn L
x
L
x
pop eKeKnn 2
1
Where
lengthdiffusion nnn DL
The appropriate boundary conditions are
0)(
)0(
poBp
kT
qV
pop
nXxn
enxnBE
n
B
n
B
kT
qV
pop
L
X
L
XX
ennBE
sinh
sinh
1
Substitute into
dx
dnqADI
p
nn
current)(emitter 0X
n
BkT
qV
n
pon
nEL
Xe
L
nqADI
BE
coth1 → current into base
BXX
Solid State Electronic Devices (Prof. Edward Yi Chang) p 7
n
BkT
qV
n
pon
nCL
Xe
L
nqADI
BE
csch1 → current get out base
The ratio of these two currents is defined as the base transport factor
n
B
nE
nCT
L
X
I
Isech
In modern BJT, nB LX
There is little recombination in the neutral base
2
2
2
11
n
BT
L
X , if nB LX
For typical BJT, if μm 30 and μm 1 nB LX
9994.0T
A transport factor that is close to 1 and
16000006.0
9994.0
B
C
I
I
T is not usually a limiting factor in current gain
The base current due to T
T
2
toduecurrent ion recombinat 12
12
BkT
qV
nA
BiE
kT
qV
n
BE
n
EnB
IeN
XnqA
eqXA
AQI
BE
BE
Where n is the e- lifetime in the base.
Solid State Electronic Devices (Prof. Edward Yi Chang) p 8
BB.. HHoollee iinnjjeeccttiioonn iinnttoo tthhee eemmiitttteerr
The dominant mechanism in limiting β in modern BJTs is hole injection into the
emitter from base. Note that this process must occur because VBE decreases the barrier
to e- flow E→B and also the barrier for hole flow B→E.
The injected hole currents in each case come directly from our analysis of long base
and short base diodes.
1
1
2
2
kT
qV
EDE
pE
ipEpEE
kT
qV
pEDE
pE
ipEpEE
BE
BE
eXN
DqAnILX
eLN
DqAnILX
The injection efficiency of the emitter is defined as
tot
nE
pEnE
nE
I
I
II
I
small) is if , (since 1
1
small) is if ,1
coth (since 1
coth1
2
ypN
np
N
ne
X
pqADI
eX
nqAD
yy
yeX
L
L
nqAD
L
Xe
L
nqADI
Eo
DE
EoEo
DE
ikT
qV
E
EopE
pE
kT
qV
B
ponB
kT
qV
B
n
n
ponB
n
BkT
qV
n
ponB
nE
BE
BE
BE
BE
Solid State Electronic Devices (Prof. Edward Yi Chang) p 9
nB
pE
DE
AB
E
B
ABEoDEpo
E
EopE
B
ponB
B
ponB
kT
qV
E
EopEkT
qV
B
ponB
kT
qV
B
ponB
pEnE
nE
D
D
N
N
X
X
NpNn
X
pD
X
nD
X
nD
eX
pqADe
X
nqAD
eX
nqAD
II
I
BEBE
BE
1
1
),(
11
1
If pEnB LXLX or ,
Then the long diode approximations replace XB or XE with Ln and Lp.
We can make close to unity by
A) Making ABDE NN
B) Making XE large or alternatively by preventing hole recombination at the emitter
contact.
C) Making XB small, this is also desirable from the point of view of increasing T
Typically, 0.999 to99.0
nB
pE
DE
AB
E
B
D
D
N
N
X
X
1
1
A current gain of 100~1000 should be achieved.
Such values are typically observed for BJT.
Solid State Electronic Devices (Prof. Edward Yi Chang) p 10
CC.. EE--BB ssppaaccee cchhaarrggee rreeggiioonn rreeccoommbbiinnaattiioonn
Note that both T and are independent of VBE, implying that the ratio of
collector to base current is a constant, independent of VBE, i.e. current level.
In practice, the ratio of the two current (IC/IB) is not independent of IC at low levels,
the dominate reason is recombination in the E-B depletion region.
We saw in our PN junction discussion that some recombination of the carriers moving
through the depletion region will occur, and that
kT
qV
Eic
BE
eWqAn
I 2
0
Re
Where 0 is the lifetime in the depletion region.
(1) kT
qVBE
e 2 dependence is important low current levels
(2) This current flows in the EB circuits and does not directly effect IC, thus as Irec
becomes important, the ratio IC/IB will change.
Summarizing of these together the current gain
regiondepletion at ion recombinat
Re
baseat ion recombinat
emitterat ion recombinat
1
nE
c
nE
nCnE
nE
pE
C
B
I
I
I
II
I
I
I
I
kT
qV
in
EBA
n
B
nED
pBABE
enD
WXN
L
X
DXN
DXN2
0
2
2
22
1
This equation is only valid for larger β.
Solid State Electronic Devices (Prof. Edward Yi Chang) p 11
Note that
(1) kT
qV
C
BE
eI over a wide range of I
(2) kT
qV
B
BE
eI at moderate currents
(3) kT
qV
B
BE
eI 2 at low level due to recombination at depletion region
Solid State Electronic Devices (Prof. Edward Yi Chang) p 12
High level effect
A. High level injection in the base
If injection levels are very high, the assumption n<<NA in the base is no longer valid.
In this case, for the base to remain quasi-neutral.
BX
B
AB
pdxqQ
xnxNx
0
and
)()()(
B. High level injection in the collector
The collector is doped lightly to obtain reasonable B-C breakdown at high level
injection, the assumption of complete depletion in the B-C depletion is no longer
valid.
If the electrons are traveling at the saturation drift velocity, sat , then at any given time,
the density of electrons in the depletion region is satsat
JxNpJ
)(
As a result, there is excess negative charge on the base side of the depletion region
and less positive charge on the collector side, the net result is to maintain charge
neutrality, the depletion region shrinks in the base side and widens in the collectors
side. As a result, the neutral base region widens )region base( , BX
Solid State Electronic Devices (Prof. Edward Yi Chang) p 13
Frequency limitation
A number of time constants inherent to the device may limit its frequency response.
1. Base transit time
In the absence of ε field in the base (NA=constant, love level injection) then the
injected e- concentration varies linearly across the base. The total charge in the base is
EBpB AXqnq2
1
The transit time across the base is simply
n
BB
B
p
n
EBp
B
B
p
nC
C
BB
D
X
X
nqD
AXqn
X
nqDI
I
q
2
2
1
current) (diffusion
2
D: average e- diffusion time in the base
If the base doping is graded, an aiding ε field speeds up the carriers, the B is
reduced by at least 2 times.
B is not usually the dominate frequency limitation.
2. Emitter base capacitance charging time
From the earlier PN diode discussion
EE
BEe
qI
kT
dI
dVr
Cje depends on the doping levels and current level (VBE) in the transistor. A rough
approximation is that
)0(2 BEje CC
where CBE(0) is the zero voltage B-E
Junction capacitance
)0(
E
2 BEjeeE CqI
kTCr
Solid State Electronic Devices (Prof. Edward Yi Chang) p 14
3. Collector capacitance charging time
The B-C junction is reversed biased and the junction impedance is very high
CRCC
where
ecapacitancregion depletion C-B:
resistance seriescollector :
C
RC
4. Collector depletion layer transit time
For moderate or high B-C reverse biases, the ε field across the depletion layer is high,
so the electrons can be assumed to move at sat
widthdepletion C-B:
2
DBC
sat
DBCD
X
X
All of time delays we considered add.
We have
DCEBtot
Cutoff frequency of the device is
tot
tf2
1