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Bipolar Junction Transistor Models
Professor K.N.Bhat
Center for Excellence in Nanoelectronics
ECE Department
Indian Institute of Science
Bangalore-560 012
Email: [email protected]
1
Bipolar Junction Transistor Modeling
Topics for presentation:
• Merits of BJT
•BJT types and structures
•Current components ,current gain and breakdown
voltage
•Ebers –Moll model for BJT and Breakdown voltage
•BJT with non uniform base region doping
•Cut off frequency and effect of base spreading
resistance
•Heterojunction Bipolar Transistor and models
2
Comparative Merits of FETs and BJTs
Parameter
Cut-Off Freq
and Transit
time
Threshold
Voltage
FETs
Channel Length
dependent
Strongly
depends upon
doping
concentration
and thickness of
the channel
layer
BJTs
Base Width
dependent
Practically
constant (diode
cut in voltage)
and depends on
the Eg of the
semiconductor
3
Comparative Merits of FETs and BJTs
Parameter
FETs
Charge
Storage
Effects
Minimum –
Device is
basically fast
TransConductance
gm
Depends on
BJTs
charge storage
reduces
Switching Speed
Highest in BJT per
(VGS- VTh), µn, unit area. Depends
upon collector
W, Cox or Cs
current which
and L
exponentially
depends on VBE/VT
4
BJT types
•Alloy Junction – Uniform base (germanium and
silicon transistors)
•Planar Junction Transistor-graded base (Silicon
transistors)
•Heterojunction Bipolar Transistor-Uniform base
and graded base (Transistors using Compound
semiconductors- Silicon/ silicon Germanium ,
AlGaAs/ GaAs)
5
Alloy Junction Transistor
6
Planar Junction diode
7
Planar Junction Transistor
8
Monolithic Transistors without Isolation
9
BJT in Integrated Circuit with Isolation
10
Bipolar Junction Transistor (Uniformly
doped regions) Current Components
WE
IC  I pC  I co
 T I pE  I co
 T ( I E )  I co
 I E  I co
T is base transport factor

is Emitter efficiency
11
Carrier Density
Distribution (BJT
biased in Active region)
peo  pneVE / VT
neo  n pe eVE / VT
12
Common Base Characteristics
IC   I E  Ico
13
Common Emitter Characteristics
IC   I B  (  1) Ico
 Change due to Early
effect
14
Base width Modulation (Early Effect)
Output resistance is reduced
15
Current gain of narrow base transistors
I B  I ne  I rec  I ne
qDne neo
 ae
 ae
WE
I c  I pc  ae
qD pb peo
W
 ae
qDne n pe eVE / VT
WE
qD pb pneVE / VT
W
2
I c D pb pnbWE D pb ( ni / N Db )WE



IB
Dne n peW
Dne ( ni2 / N Ae ) W
D pb N AeWE
 N Ae dx
D pb E


Dne N DbW
Dne  N Dbdx
B

High when
total emitter
doping is high
16
Collector –Base Junction Breakdown
Voltage , BVCBO
•Junction breakdown takes place when the
carrier multiplication factor ‘M’ becomes
infinite.
• ‘M’ depends upon the initiating carrier and is
related to the applied voltage, V and the
breakdown voltage BVCBO.
M
1
 V

1

BV
CBO 

n
n=6 for PNP transistor
n=4 for NPN transistor
17
Maximum sustaining voltage BVCES in
the Common emitter configuration
IC   I B  (  1) Ico
At VCES , IC tends to infinity. This is
possible when  tends to infinity
because in CE mode IB is constant


,
1 
  , when   1
  (  T ) M  0 M
 At VCES , 0 M  1
18
 V

1
0 M  1 gives, 0 
 1

M
BVCBO 

n
 V


  1  0
 BVCBO 
n
BVCBO
1/
n
VCES  BVCBO (1  0 )

1/
n
(1   )
In high Voltage transistors the  is
deliberately made small to achieve VCES
as close to BVCBO as possible
19
Ebers –Moll Equations for BJT
Transistor Operating modes:
1.Normal mode -active , saturation and cut off .
2. Inverse mode – emitter as collector and
collector as emitter
EBERS –MOLL model gives a set of
equations encompassing all the four
operating regions of operation in circuit
simulations
20
Transistor operating in Normal
Mode or Forward active mode
21
Transistor operating in Inverse
Mode or Reverse active mode
22
Transistor operating in Saturation Mode
23
Ebers Moll Equations Valid for all
combinations of VEB and VCB
Here we have
24
I E   IF   I I R
25
NPN-Transistor having Non-uniformly
doped Base P-region (graded base )
Base Region
26
The doping gradation
gives rise to an
electric field E(x)
which arises to
counter the diffusion
of holes. E(x) aids the
flow of electrons in the
x direction
dp p
In thermal equilibrium J p  qp p p E  qD p dx  0,
Dp
p

D p 1 dp p
 E( x) 
 p p p dx
kT
 VT , p p  N A
q
VT dN A
VT
E( x) 

N A dx
L
27
•Carrier transport is by drift and diffusion
in Graded base transistor
•Velocity of carriers is three to four times
higher compared to transistors with
uniformly doped base region
W
velocity
1 velocity
t 

t
W
•Transit time of carriers ,
•Cut off frequency,
t 
•Smaller base width is required for higher
cutoff frequency
28
Base spreading resistance rbb ' ( rb in figure below)
depends upon base region doping concentration NA
and base width W
29
Need for modifications in BJT
For high speed, WB should be
reduced . This increases rbb’
affecting the maximum operation
frequency, fm , at which power
gain is unity . fm is given by
fm 
fT
8 C jc rbb'
30
Conflicting Requirements for fT and fm
•Cutoff frequency fT can be increased by
reducing base width ‘W’. This increases rbb '
and lowers fm
•To improve fm , rbb ' should be reduced
31
r bb’ is the base spreading resistance and is
proportional to the sheet resistance which varies
inversely as total integrated doping
concentration (= NAW) in the base region.
NA should be increased when WB is reduced so
that rbb’ does not increase . It leads to
(1) increase in CTE , (2) reduction in β and (3) fall
in DnB
These conflicting requirements are met using an
emitter region of wider band gap material. This
BJT is the Heterojunction Bipolar Transistor
(HBT)
32
Heterojunction Bipolar Transistor (HBT)
First HBT in the history of BJT
n-AlGaAs / p-GaAs / n+GaAs HBT
AlGaAs
B
E
n
GaAs
p
GaAs
n
n+ collector
33
C
For PNP transistor we have seen
2
I c D pb pnbWE D pb ( nib / N Db ) WE



2 / N )W
IB
Dne n peW
Dne ( nie
Ae
2
D pb N AeWE nib

Dne N DbW n2
ie
Similarly for NPN transistor , we have
2
I c Dnb N DeWE nib


IB
D pe N AbW n2
ie
34

2
DnB NDTE niB
2
DpE NATB niE
NDTE 
;
ND (x) dx
Emitter
EgB kT
DnB NDTE e

EgE
DpE NATB e

NATB 

NA (x) dx
Base
kT
 DnB NDTE  Eg kT

e

 DpE NATB 


Eg  EgE  EgB 
35
Typically , Eg  0.3eV , e
Eg kT
 1.63 x 105
NDTE
DnB
1
When,  

and
 2.5
NATB 200
DpE
1
5
  2.5 x
x 1.63 x 10  2038
200
36
n-AlGaAs / p-GaAs / n+GaAs HBT
E
0.2m
B
n+ > 1018/cm3
GaAs
0.3m Emitter
AlGaAs
ND =5x1017/cm3
0.15m GaAs base
0.5m GaAs collector
P=1018/cm3
n=1018/cm3
N+GaAs substrate
C
37
AlGaAs /GaAs /GaAs HBTs fabricated at
BELL Labs showed the following:
•very low values of  =30
• Higher values of  were observed in Devices with
larger areas.
•The  increased from 30 t0 about 1800 when the
surface of the base region was passivated by
chemical treatment to saturate the dangling bonds
with sulfur . But the  values were unstable .
•Several approaches have been used to stabilize the
. The most successful one has been chemical
treatment with (NH4)2Sx and protect with PECVD
silicon nitride
38
Silicon Germanium HBT (SiGe HBT)
WB
n
Si
p
SiGe
nSi
n+
Si
• Band gap of Si1-xGex depends upon x.
• Strained layer Si1-xGex without
dislocations can be realized with thin
layers of base
39
Strained Layer Epitaxy
for Lattice mismatched
materials
Possible means of growing
lattice – mismatched materials.
40
Solid Line : Calculated
thickness above which it
becomes energetically
favorable to form misfit
dislocations in strained layer
GeSi grown on Si
Points: experimental data for
low temperature MBE
growth.
Dashed Line : Trend
calculated for simple model
of kinetically limited defect
formation
41
Calculations showing the diagrammatic effect of
strain upon semiconductor band gaps
Unstrained Gex Si1-x
Strained Gex Si1-x
on Unstrained
Gex/2 Si1-x/2
Strained Gex Si1-x
on Unstrained Si
Strained Si on
Unstrained Gex Si1-x
42
Benefits of SiGe HBT over Si BJT
• Collector Currents IC is larger
for a given VBE
2
qDnB niB
VBE VT
C 
e
WB
 N A  x  dx
0
 E gB kT
2
niB  e
43
Benefits of SiGe HBT over Si BJT
(Contd….)
• IC increase improves 
• IC increase decreases the
emitter charging time. This
improves the switching
speed.
44
Effect of grading the band gap
in the Base Region
n
p
0
n
x
E
Eg(0)
Eg(x)
WB
Eg(WB)
Eg(x) = Eg(0) - Eg(x)
45
Electric Field due to bandgap gradation is
given by
dE g
dx
1 dE g
q dx

. For a linear gradation
E g  0   E g WB 
WB

E g
WB
For E g = 0.15 eV and WB = 0.1 m
Electric Field = 0.15/10-5 = 15 KV / cm
Cut off frequencies up to 200GHz have been achieved
46
Summary
• BJTs are still popular for achieving better
driving capability particularly when the load is
capacitive.
•Ebers Moll model enables us to estimate the
currents for all modes of BJT operation.
•Base region can be reduced and doping
concentration in the base can be increased with
HBTs.
• Base region with graded doping and graded
band gap lead to higher cut of frequencies due
to reduction in transit time as a result of the
47
built in electric field