9-bjt
TRANSCRIPT
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 1
9-BIPOLAR JUNCTION TRANSISTOR (BJT)
Strengths1. Threshold Voltage controlled byEg (only very weak
dependence on doping and process parameters)
2. Very high transconductance (gm) and high nonlinearity
- Lower voltage swing in logic
- Lower sensitivity to parasitics
3. Vertical device (diffusion, ion implantation and epitaxy)
- easier to achieve small dimensions vertically than
laterally (lithography)
4. High current/unit area High drive capability for driving long
off chip lines or for high current devices, such as LEDs or lasers
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 2
BIPOLAR JUNCTION TRANSISTOR (BJT)
Weaknesses
1. High Power
- relatively low levels of integration
2. No effective complementary circuit technology
3. Device based upon minority carriers
- charge storage and diffusion rather than drift
4. Difficult compromises for device optimization
- Base resistance: RC time constants and transit time favor
a very thin, highly doped base
- high injection efficiency requiresNE>>NB
- Bandgap shrinkage, lower defect densities and E-Bcapacitance all favor moderate emitter doping
5. Far greater processing complexity, larger number of mask
levels with tight alignment tolerances on high performance
devices.
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 3
I. Basic Structure and Band Diagrams
Basic bipolar transistor structure: Two pn junctions J1 and J2are placed back-to-back a distance Wapart, forming an n-p-n
structure.
The simple, idealized transistor shown below has doping
density of 1018 cm-3 in the emitter and collector and 1016 cm-3
in the base.
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 4
C
B
E
Cross section, simplified model and symbol of a double
diffused discrete pnp transistor
Structure and Model of pnp Bipolar Transistor
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 5
C
B
E
Cross section, simplified model and symbol of an integrated
circuit npn bipolar transistor
Structure and Model of npn Bipolar Transistor
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 6
The figures on the left show
(i) energy-band diagrams and
(ii) electron-density
for the ideal transistor sketched on
page 1 for the following
conditions:
Equilibrium Cutoff
Saturation Active
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 7
(a) thermal equilibrium (zero bias)
(b) both junctions reverse-biased (cutoff mode)
(c) both junctions forward-biased (saturation mode)
(d) J1 forward-biased and J2 reverse-biased (active mode)
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 8
Basic Operation in Forward Active Region
The E-B junction is
forward biased and
the C-B junction isreverse biased
N+ P NE C
B
WB
x
x
x
V
_
Ec
Ev
EF
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 9
Doping profile in a realistic IC npn transistor
Collector is formed by epitaxy
and base and emitter by ion
implantation
N+ P N N+E C
holes for recombinationand injection into emitter
B
~ 0.7 volts
emostof the
e
WB
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 10
Notation:
The notation used in these notes is for an npn BJT, which isopposite that used in Pierret. Terms used are defined as follows:
NE= NDE NB= NAB NC = NDC
DE = DP DB= DN DC = DP
E = p B = n C = pLE = LP LB = LN LC = LP
pE0 = pn0 nB0 = np0 pC0 = pn0
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 11
The BJT operates basically as follows:
1. An external voltage is applied to forward bias the B-Ejunction ( 0.7 volts).
2. Electrons are injected from the emitter into the base
(holes are also injected from the base into the emitter, but
their numbers are much smaller becauseNDE> NAB).
3. If WB
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 13
Ec
Ev
EF
0= dx
dpqDpqJ BxBBp
dx
dp
pq
kT
dx
dp
p
D
B
Bx
11=
(1)
To derive the basic relationship for electron current flowing
between the E and C, first assume the device current gain is
high. The hole current in the base is small.
E
E
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 14
Thus for uniform doping in the base, Ex 0 and the electrons
traveling through the base will move only by diffusion.In a modern ion implanted base transistor, dp/dx 0, henceEx 0 . The direction of this field aids electron flow from E toC, and retards electron flow from C to E.
The electron flow between E and C is given by
+=
+=
+=
dxdnp
dxdpn
pqD
dx
dnqD
dx
dpn
p
kT
dx
dnqDnqJ
B
BB
BxBBn
E
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 15
where W= the width of the quasi neutral base region
(JBn is pulled outside the integration by assuming no
recombination of electrons in the base, i.e., JBn = constant)
( ) ( )0
)(00
pnWpn
pnddxqD
pJ
dx
pnd
p
qD
WW
B
Bn
B
=
=
=
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 16
From diode analysis, the pn products at the edge of the
depletion regions are given bypn x = 0( )= ni
2eqVBE /kT
pn xB( ) = ni2eqVBC/kT
JBn =qni
2e
qVBC / kT eqVBE / kT[ ]p
DBdx
0
W
In = Is eqVBC/kT e
qVBE /kT
AssumingDn is constant in the base
(2)
B
Bis
Q
DAnqI
22
=
(3)
where
(4)
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 17
=W
B dxpqQ
0
(5)
is called the base Gummel number.
(6)
A = E-B cross-sectional area
1. Only one of the two exponential terms is important inforward or reverse active bias region. When the deviceis in saturation, both junctions are forward biased andboth terms must be included.
2. The quantity
which is the total undepleted charge in the base
=W
B
W
B dxNdxp
q
Q
00
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 18
( )
( kTqVkTqVB
Bi
kTqVkTqV
B
BiBn
BCBE
BCBE
eeQ
DAnq
eeWN
DqAnI
//
22
//
2
=
=
(7)
QB is the total integrated base charge (atoms/cm2). SinceI
1/QB, it is important to minimize QB, i.e., use low doping levelsin the base (this is a good strategy to achieve maximum dc
current gain, but we will see that this does not work for high
frequencies).
If the base is uniformly doped, E = 0, QB = q NB W
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 19
A. Recombination in the Neutral Base Region
Some of the electrons traversing the base will recombine withmajority carrier holes. (This is usually unimportant in modernIC BJTs).
III. Current Gain
A number of factors can contribute to base current in a BJT. Weconsider them individually.
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 20
If we assume that the base is uniformly doped so that Ex = 0,then the electron transport and continuity equations are
02
2
=
=
B
BoBBB
BBn
nn
dx
ndD
dx
dnqADI
NN +
nB
nB0pC0pE
pE0
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 21
As discussed in the case of the P-N junction, the generalsolution to these equations is
whereLB = (DBB)1/2 = diffusion length
The appropriate boundary conditions are
With these boundary conditions, the solution is
BB LxLx
BBeKeKnn
/
2
/
10+=
( )
( ) 0
0/
2
/
0
=
===
Wxn
eN
nenxn
B
kTqV
B
ikTqV
BBBEBE
nB nB0 eqVBE / kT 1( )
sinh Wx( )/ LB[ ]sinh W / LB( )
(8)
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 22
Excess Minority Carrier Profiles for Different W/LN
Ratios
Most minority carriers
make it across the base if
WLN. In todays BJTs,
W is typically
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 23
The emitter and collector electron currents are
(9)
(10)
The ratio of these two currents is defined as the base transportfactor.
InE = In x = 0( ) =qADBnB0
LBeqVBE / kT 1( )coth W
LB
InC = In x = W( ) =qADBnB0
LBe
qVBE / kT 1( )csch WLB
(11)
BnE
nC
T
L
W
I
Isech==
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 24
(12)
In a typical modern BJT, W 1 m and LB 30 m so that
T 0.9994. T is NOT a limiting factor in current gain.
Using Eq. 9, 11 and 12 the base current due to Tis
(13)
2
2
2
11
B
T
L
W
IBREC= InE InC
= 1T( )In qAni2W
2NBBeqVBE / kT 1( )
In modern IC BJTs,xB
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 25
where B = electron lifetime in base =
B. Hole Injection into the EmitterThe dominant mechanism in limiting in modern BJTs ishole injection from B into E. This process occurs becauseVBEnot only decreases the barrier to electron flow from E toB, but also the barrier for hole flow from B to E.
xE >> LE xE >= for1
/
2
( ) EEkTqVEE
EipE Lxe
xN
DqAnI BE
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 27
If W>>LB or xE>>LE, then WorxE is replaced withLB orLE.
This equation is only approximately correct in IC structuresbecauseNB andNEare not constant. Typically, 0.98 which
implies a current gain 50. Such values are typically observed in
IC BJTs.
is maximized (close to unity) by
1. Making NE >>NB
2. MakingxElarge or alternatively by preventing hole
recombination at the emitter contact.
3. Making Wsmall. This is also desirable for increasingf.
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 28
Summarizing our discussion of current gain,
(17)
In modern BJTs Tis nearly 1 and is the main factor
limiting the performance.
(18)
By combining Eq. (12) and (16) and making appropriate
approximations it can be shown that
TpEnE
nE
nE
nC
pEnE
nC
E
CF
III
II
III
II =
+
=
+
==
=IC
IB
=
IC
IE I
C
=
F
1 F
WND
LND
L
W
LND
WND
BE
EEB
BEEB
BE
+=
12
2
1
The main parameter to achieve high gain is the ratio ofNE/NB
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 29
Deviations from the IdealBase Width Modulation
Common Base Configuration
EB o sEB o s
p Collect.
n+ Base
p+ Emit.
onstant ase w t ,independent of V CB
VEB
VCB
IE
Base width
modulation--decrease in W
with bias VCB
n+ Base
p o ect.
p+ Emit.
VEB
More depletion withVCB: smaller x B
IE
VCB
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 30
Base Width ModulationCommon Base Configuration
Ideal Experimental
The output characteristics are nearly ideal in spite of the base widthmodulation because the emitter current is controlled or fixed, hence
there is no regenerative feedback and increase in both the collector
and emitter current that is observed in the common emitter
configuration.
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 31
Deviations from the IdealBase Width Modulation
Base width
modulation--
decrease in Wwith bias VCB
EB o s
n+ Base
IC
p o ect.
p+ m t.
VEB
More depletion withVCB: smaller xB
Decreasing W
BL
Wcoth
InE=qADBnB0
LB
eqVBE / kT1( )coth W
LB
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 32
BJT Non-idealities
Common Emitter Configuration
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 33
Base Width Modulation: Early
Voltage
The Early Voltage VA is a measure of how independent
the base width, W, is from VCB . Small |VA| means large
base width modulation.
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 34
WND
LND
L
W
LND
WND
BE
EEB
BEEB
BE
+=
12
2
1
Base Width Modulation: Early Voltage
As VCincreases, the reverse bias across the B-C increases, the
depletion region widens. Hence the neutral base width W ,
andIC
The Early effect is usually modeled as
IC = IS eqVBE / kT 1( ) 1 +
VCE
VA
(19)
Where
Si
BBA
WqNV
2
is known as the Early voltage
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 35
Breakdown due to Punch-thru
When the base becomes depleted, the base resistance , with
large voltage drop, hence, the base potential no longer controlsthe E-B junction voltage. Carriers are injected from emitter tocollector with exponential dependence on VEC, not VEB. Thisseldom happens in modern BJTs because the base is more heavilydoped than the collector so depletion extends into the collector.
This is an identical process to that
describing extension of the drain
depletion layer thru to the source in a
MOSFET.
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 36
Punch-thru Breakdown
n+ Base
IC
p Collect.
p+ Emit.
VEB
VCB
VCB (Volts)
unc t rougbreakdown: base
completely depleted
n+ Base
IC
p Collect.
p+ m t.VEB
VCB
Not as common as avalanche breakdown in modern BJTs
VCE (Volts)
Common Base Common Emitter
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 37
The large shift in the inputIB-VEB characteristic is because, with very
low VEC, the base current is due to injection from the base into the
collector because the built-in voltage of the B-C junction is lower.
The increase in the output characteristic at low VECis due to basewidth modulation and increase in due to an increase in
The sharp reduction in breakdown voltage is due to either punch
through of the collector to the base and reduction of the E-B junction
barrier by the C-B voltage or by amplification ofANYimpact ionized
carriers in the C-B junction which drift back into the base region and
become amplified. This occurs because there is very little
recombination in the base, hence the impact ionized carriers areinjected from the base into the emitter, causing an additional injectionoftimes this number of carriers from the emitter into the base and
these extra injected carriers then make it to the collector, increasing Ic.
dpndx
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 38
Preventing Base Width Modulation
(and Punch-Thru)
Base width modulation (and its extreme: punch-through) is
caused by the CB depletion region growing into the base
with applied bias.
To prevent this, collector doping should be much lower than
base doping, so the depletion region extends almost entirely
into the collector rather than into the base.
n+ Base
IC
p co ect.
p+ Emit.
VEB
VCB
n+ Base
IC
p o ect.
p+ Emit.
VEB
VCB
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 39
Avalanche BreakdownCommon Emitter Configuration
Breakdown!
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 40
Avalanche Multiplication and Breakdown
P-N-P transistor
Base current is held constant in
the common emitter
configuration, so the only place
that excess electrons in the base
(4) can go is into the emitter.
This produces an internal bias
that causes an injection of holes,
Ip = In, which is regenerative
and leads to a much lower
breakdown voltage
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 41
IC =dc
1dc
IB +1
1dc
ICB0
IC =dc
1 Mdc
IB +1
1 Mdc
ICB0
The common expression for collector current
can be modified to account for the avalanche multiplication andresulting emitter injection by replacing dc by Mdc
Since dc ~ 0.99, M need only be ~1.01 to haveIC.
Recall in PN junction avalanche, M 10-100 beforeI.
Lower voltage for the onset of avalanche breakdown.
Collector doping must be light to prevent avalanche
breakdown. (Also prevents base width modulation.)
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 42
IV. Low and High Current Level Effects on Theoretically,Tand are independent ofVBE, implying thatthe ratio of collector current to base current (i.e., current gain) is a constant, independent ofVBEorIC. In practice, theratio of the two currents is NOT independent ofIC.
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 43
A. B-E Depletion Region Recombination
At low current levels, the dominant reason for the reduced isrecombination in the B-E depletion region.
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 44
In the P-N junction discussion, it was shown that some
recombination of the carriers moving through the depletion
region will occur, and that (19)
where o = lifetime in the depletion region.
1. This current flows in the B-E circuit and does not directlyaffectIC. Thus asIRECbecomes important, the ratioIC/IBdecreases.
2. dependence important at low current levels.
E B C
einjection
recombination
holeinjection
*
IREC=qAniWE
o
eqVBE/2kT
kT
qVBE
2exp
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 45
High Current Effects
B. High Level Injection in the BaseE B C
einjection
NdNa + n
If injection levels are very high, the assumption of n
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 47
If the electrons are traveling at the saturated drift velocity,vsat, then at any given time, the density of electrons in the
depletion region isJ/qvsat, hence the net charge density is
As a result there is excess negative charge on the base side ofthe depletion region and less positive charge on the collectorside. The net result is that to maintain charge neutrality thedepletion region shrinks in the base side and widens in thecollector side. As a result the neutral base region widens.This phenomenon is first important in the collector sidebecause it is usually the most lightly doped.
andW
= N x( )J
qvsat
While the increase in Wdecreases to some extent, it has a fargreater impact on high frequency performance because the transittime across the C-B depletion region increases significantly.
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 48
D. Base Resistance
The effective emitter bias becomes VBE- IBRB
IC = IS exp qVBE IBRB
kT
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 49
Effect of Base Resistance
Base resistance
produces a completely
non-exponentialIC-VBEcharacteristic as
compared with either
ideal injection or G-R in
the E-B depletion
region.
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 50
E. Current Crowding
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 51
The previous figure shows a pnp transistor. AsIB andICincrease, the voltage drop acrossRB becomes significant.
This means that the effective VBEacross the active (center)portion of the device is not as great as the externally appliedVBE. The edge of the emitter thus has the highest electroncurrent density (current crowding). This plays a double roleas the bandgap of the material shrinks with increasedtemperature, further increasing the injection around theemitter periphery. The total collector current decreases belowthe ideal exp(qVBE/kT) behavior.
To minimize the impact of this
(1) The emitter should be made narrower. For higher currentcapability multiple emitters can be used in a single base.
(2) In the extrinsic base region a N+ diffusion should be done.
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 52
Heterojunction Bipolar Transistor (HBT)
Motivation:
Reduce IEp by making
hole injection into the
emitter more difficult.
Solution: Use differentmaterials with different
bandgaps: Barrier to hole
injection.
e
E mi tt er Ba se
Ec
Ev
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 53
Heterojunction Bipolar Transistor (HBT)Heterojunction E B C
Key feature is that the E-B barrier
for holes is much larger than that
for electrons
If we go back to eqs. (7) and (14) used to calculate the injectionefficiency, but do not cancel out the ni
2 terms since they will be
different when you have an emitter and base with differentEgs,
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 54
HBT Current Gain
+
=
2
2
1
1
iB
iE
E
B
EB
E
n
n
N
N
L
W
D
D
the injection ratio becomes
~
1~DB
DE
LE
W
NE
NB
niB
niE
2
and ifis limited by injection efficiency, it becomes
and ifEg = 0.356 eV, then
niB
niE
2
=
10
6
which meansNB can be 100-1000NE and we still have very
high current gain.
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 55
Big Wins for HBTs
1. Eliminates base width modulation because depletionregions are in the more lightly doped emitter and collector
regions
2. Current gain limited only by recombination in the E-B
junction or the base
3. Current crowding and base resistance are both greatly
reduced because of high base doping
4. Completely eliminates Punch-through due to high base
doping
5. Improved high frequency performance from decreased base
resistance and E-B capacitance
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 56
VI. High Frequency Limitations
A number of time constants inherent to the device may limit
its frequency response.
A. Base Transit Time
How long does it take from the time a voltage is applied at the
input (E-B) until a voltage appears at the output (CB) ?
E B C
np
~0
W
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 57
In the absence ofEfields in the base (NB = constant, low levelinjection), then the injected electron concentration varies
linearly across the base The total electron charge in the base is
Since
The transit time across the base is simply
qB =1
2qAnBxB
= 12qAnB0 e
qVBE/ kT( )W
IC =qADnnB0
WeqVBE/ kT 1( )
BC
BB
D
W
I
q
2
2
= (21)
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 58
If the base doping is graded (typical in IC BJTs), an aiding E
field speeds up the carriers and B is reduced. Also, underhigh level injection, to maintain base neutrality, the holeconcentration in the base and has a gradient similar to theelectron gradient. This sets up an Efield which also speedsup the electron transit. B is usually NOT the dominantfrequency limitation in modern BJTs.
B. Emitter Capacitance Charging Time
E B C
re
Cje
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 59
From the earlier pn diode discussion,
Cje depends upon the doping levels and current levels (VBE) in
the transistor. A rough approximation is that Cje 2 CBE(0)
where CBE(0) is the zero voltage B-E junction depletion
capacitance.
(22)
C. Collector Capacitance Charging Time
re = dVBEdIE
kTqIE
E = reCje kT
qIE2CBE 0( )
Rc
C
E
B
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 60
The B-C junction is reverse biased so the junction impedance
is very high.(23)
where
RC = collector series resistance
C = B-C depletion capacitance
D. Collector Depletion Layer Transit Time
For moderate or high B-C reverse biases, the Efield across
the depletion layer is high, so the electrons can be assumed to
move at SAT
C = R CC
SAT
BC
D
W
2 (24)
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 61
All of the time delays we have considered add, so that
(25)
The cutoff frequency of the device is simply
(26)
This is approximately the frequency at which is reduced to 1.Above this frequency, the device is not useful as an amplifier.
TOT
B+
E+
C+
D
fT =1
2TOT
Where WBC = B-C depletion width
The factor of 2 in the denominator is one of the most
erroneously quoted equations in semiconductor device physics.
It arises because the carriers are moving by drift and a current
starts to appear at the output when the carriers just enter the
base side of the B-C depletion region
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 62
VII. Ebers-Moll Model
(27)
(28)(29)
R R
E C
E CF F
B
B
F=
ESe kTqVBE
1 R=
CSe kTqVBC
1
IE =IF +RIR
IC=
FIF IR
IB = 1F( )IF + 1R( )IR
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where
F= forward alpha
IC/IE ifVBEis +ve and VBCis -veR = reverse alpha IE/IC ifVBCis +ve and VBEis -ve
IES= emitter reverse saturation current
ICS= collector reverse saturation current
The Ebers-Moll model may be used under all junction bias
conditions (i.e., cut-off, forward active, reverse active and
saturation) to estimate the terminal currents.
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 64
VIII. Hybrid ! Equivalent CircuitA useful small signal, AC equivalent circuit for the BJTs inforward active region is shown below.
The parameters are defined as follows
(30)gm = transconductane=dIC
dVBEqIC
kT
B
E
C
Cd + Cje
C
m
g vbe
rb
r
vbe
+
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 65
Cd= Diffusion capacitance of the B-E Junction (due tostored minority carriers)
r = base/emitter resistance=dVBE
dIB
gm
Cje = depletion capacitance of B- E junction
C= depletion capacitance of B- C junction
=
dqB
dVBE=
dqB
dIC
dIC
dVBE= Bgm
(31)
(32)
The DC current gain is 0 =IC
IB= gmr
Considering only the input E-B capacitance, the AC gain is
=0
1+ jrC
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 66
The AC gain decreases to 0.7070 when orrC =1
f=
1
2rC
A more widely used measure is when the current gain goes to 1
rC = 0 = gmr and
f =gm
2C
1
2EC
Even if the current gain is less than unity, the transistor can still
produce power gain due to the impedance transformation. The
unity power gain or maximum frequency of oscillation is
fmax =f
8rBCBC
12
This is the performance parameter
which is dramatically improved by
HBTs because of the ability to heavily
dope the base region and lower rB
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 67
IX. Bipolar Transistor Scaling
The intrinsic device is vertical. Scaling of lateral dimensions asconsidered in MOS transistors does not improve the intrinsic
device, but will improve the packing density and reduce the
parasitic capacitances and resistances. Scaling of the intrinsic
device is achieved by reducing the base width WB.
PARAMETER 1980 1985 1990
(1) Emitter Width (m) 3 1.5 0.8
(2) Base Width (m) 0.3 0.15 0.07
(3) fT(GHz) 1 10 30
(4) ECL gate delay (psec) 500 100 30
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 68
Bipolar Transistor Evolution
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Polysilicon Emitter
Short emitter or complete
polySi emitter
EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 70
The emitter injection efficiency is degraded by the carriers
injected from the base into the emitter. The emitter width in amodern BJT is thin, which increases speed and reduces
parasitic resistance. However, a thin emitter increases the
gradient in the minority carrier concentration. The increase in
the gradient increases the B-E back injection current, which in
turn decreases the emitter injection efficiency and decreases the
common emitter current gain. In modern bipolar transistors an
n+ polysilicon emitter is inserted between the metal contact and
the thin n+ single crystal silicon emitter region. As a first
approximation to the analysis, we may treat the polysilicon
portion of the emitter as low-mobility silicon, which means that
the corresponding diffusion coefficient is small.
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EE 216 Principles and Models of Semiconductor Devices (Autumn 2005) Prof. J. S. Harris 71
Assuming that the neutral widths of both the polysilicon and
single-crystal portions of the emitter are much smaller than
the respective diffusion lengths, then the minority carrier
distribution functions will be linear in each region as shown
in the figure. Both the minority carrier concentration and
diffusion current must be continuous across the
polysilicon/silicon interface.
SinceDEpoly
dpEn+
dx