Lecture 26
OUTLINE
The BJT (cont’d)
•
•
•
•
•
Breakdown mechanisms
Non-ideal effects
Gummel plot & Gummel numbers
Modern BJT structures
Base transit time
Reading: Pierret 11.2-11.3, 12.2.2; Hu 8.4,8.7
BJT Breakdown Mechanisms
• In the common-emitter configuration, for high output voltage
VEC, the output current IC will increase rapidly due to one of
two mechanisms:
– punch-through
– avalanche
EE130/230M Spring 2013
Lecture 26, Slide 2
Punch-Through
E-B and E-B depletion regions
in the base touch  W = 0
As |VCB| increases,
the potential barrier
to hole injection
decreases and hence
IC increases
EE130/230M Spring 2013
Lecture 26, Slide 3
Avalanche Multiplication
• Holes are injected into the base [0], then PNP BJT:
collected by the B-C junction
– Some holes in the B-C depletion region have
enough energy to generate EHP [1]
• Generated electrons are swept into the
base [3], then injected into emitter [4]
– Each injected electron results in the injection of
IEp/IEn holes from the emitter into the base [0]
 For each EHP created in the C-B depletion region by impact ionization,
(IEp/IEn)+1 > bdc additional holes flow into the collector
i.e. carrier multiplication in the C-B depletion region is internally amplified
VCE 0
where VCB0 = reverse breakdown voltage of the C-B junction
VCB 0

( b dc  1)1 / m 2  m  6
EE130/230M Spring 2013
Lecture 26, Slide 4
Non-Ideal Effects at Low VEB
• In the ideal transistor analysis, thermal R-G currents in the
emitter and collector junctions were neglected.

I Ep
I Ep  I En  I R G
• Under active-mode operation with small VEB, the thermal
recombination current is likely to be a dominant component
of the base current
 low emitter efficiency, hence lower gain
This limits the application of the BJT for amplification
at low voltages.
EE130/230M Spring 2013
Lecture 26, Slide 5
Non-Ideal Effects at High VEB
• Decrease in bdc at high IC is caused by:
– high-level injection


qAni2 DB qVEB / kT
IC 
e
1
WN B
– series resistance
– current crowding
EE130/230M Spring 2013
Lecture 26, Slide 6
Gummel Plot and bdc vs. IC
bdc
bdc
EE130/230M Spring 2013
From top to bottom:
VBC = 2V, 1V, 0V
Lecture 26, Slide 7
Gummel Numbers
For a uniformly doped base with negligible band-gap narrowing,
the base Gummel number is
N BW
GB 
DB
(total integrated “dose” (#/cm2) of majority carriers in the base, divided by DB)



1


qAni2 DB qVEB / kT
qAni2 qVEB / kT
IC 
e
1 
e
1
WN B
GB
Emitter efficiency
1
ni E 2 D N W
E
B
ni B 2 DB N E WE
1

GB
1
GE
GE is the emitter Gummel number
EE130/230M Spring 2013
Lecture 26, Slide 8
Notice that
b dc 
1
ni E 2 D N W
E
B
ni B 2 DB N E LE

 
1 W 2
2 LB
GE

GB
In practice, NB and NE are not uniform, i.e. they are functions of x
The more general formulas for the Gummel numbers are
W
GB  
0
W
GE  
0
EE130/230M Spring 2013
2
ni N B ( x)
dx
2
ni B DB ( x)
2
ni N E ( x)
dx
2
ni E DE ( x)
Lecture 26, Slide 9
Modern NPN BJT Structure
Features:
• Narrow base
• n+ poly-Si emitter
• Self-aligned p+ poly-Si base contacts
• Lightly-doped collector
• Heavily-doped epitaxial subcollector
• Shallow trenches and deep trenches filled with SiO2
for electrical isolation
EE130/230M Spring 2013
Lecture 26, Slide 10
Poly-Si Emitter
•
bdc is larger for a poly-Si emitter
BJT as compared with an allcrystalline emitter BJT, due to
reduced dpE(x)/dx at the edge
of the emitter depletion region
Continuity of hole current in emitter:
dpE1
dpE 2
 qDE1
 qDE 2
dx
dx
dpE1 DE 2 dpE 2  E 2 dpE 2


dx
DE1 dx
 E1 dx
(1poly-Si; 2crystalline Si)
EE130/230M Spring 2013
Lecture 26, Slide 11
Emitter Gummel Number w/ Poly-Si Emitter
2
2
ni N E
ni N E (WE )
dx  2
WE , poly
2
ni E DE
ni E (WE ) DE
WE
GE  
0
WE

0
ni N E
ni N E (WE )
dx  2
2
ni E DE
ni E (WE ) S p
2
2
where Sp  DEpoly/WEpoly is the surface recombination velocity
2
ni  WE 1 

For a uniformly doped emitter, GE  N E 2 
niE  DE S p 
qni A qVEB / kT

IB 
e
 1
GE
2
EE130/230M Spring 2013
Lecture 26, Slide 12
Emitter Band Gap Narrowing
2
niB N E
b dc  2
niE N B
To achieve large bdc, NE is typically very large, so that band gap
narrowing is significant (ref. Lecture 3, Slide 20).
n N c N v e
2
iE
 EGE / kT
niE2 ni2 e EGE / kT
EE130/230M Spring 2013
 Nc Nve
 ( EG  EGE ) / kT
EGE is negligible for NE < 1E18/cm3
N = 1018 cm-3: EG = 35 meV
N = 1019 cm-3: EG = 75 meV
Lecture 26, Slide 13
Narrow Band Gap (Si1-xGex) Base
2
niB N E
b dc  2
niE N B
To improve bdc, we can increase niB by
using a base material (Si1-xGex) that has
a smaller band gap
• for x = 0.2, EGB is 0.1 eV
This allows a large bdc to be achieved
with large NB (even >NE), which is
advantageous for
• reducing base resistance
• increasing Early voltage (VA)
EE130/230M Spring 2013
Lecture 26, Slide 14
courtesy of J.D. Cressler (GATech)
Heterojunction Bipolar Transistors
a) Uniform Ge concentration
in base
b) Linearly graded Ge
concentration in base
 built-in E-field
EE130/230M Spring 2013
Lecture 26, Slide 15
Example: Emitter Band Gap Narrowing
If DB = 3DE , WE = 3WB , NB = 1018 cm-3, and niB2 = ni2, find bdc for
(a) NE = 1019 cm-3,
(b) NE = 1020 cm-3, and
(c) NE = 1019 cm-3 and a Si1-xGex base with EGB = 60 meV
(a) For NE = 1019 cm-3, EGE  35 meV
niE2  ni2 e35meV / 26meV  3.8ni2
1019  ni2
DBWE N E ni2
b dc 

 9  18
 23.6
DEWB N B niE2
10  3.8ni2
(b) For NE = 1020cm-3, EgE  160 meV:
niE2  ni2 e160meV / 26meV  470ni2
10 20  ni2
DBWE N E ni2
b dc 

 9  18
 1.9
DEWB N B niE2
10  470ni2
(c) niB2  ni2eE
gB / kT
EE130/230M Spring 2013
 ni2e60meV / 26meV  10ni2
Lecture 26, Slide 16
b F  236
Charge Control Model
A PNP BJT biased in the forward-active mode has excess
minority-carrier charge QB stored in the quasi-neutral base:
pB ( x, t )  pB (0, t )1  Wx 
qAWpB (0, t )
QB  qA  pB ( x, t )dx 
2
0
W
In steady state,
EE130/230M Spring 2013
dQB
0
dt

Lecture 26, Slide 17
iB 
dQB
QB
 iB 
dt
B
QB
B
Base Transit Time, t
p B ( x, t )
iC   qADB
x
x W
qADB p B (0, t )

W
qAWpB (0, t )
QB 
2
2 DB QB QB
iC 

2
W
t
W2
t 
2 DB
• time required for minority carriers to diffuse across the base
• sets the switching speed limit of the transistor
EE130/230M Spring 2013
Lecture 26, Slide 18
Relationship between B and t
• The time required for one minority carrier to recombine in the
base is much longer than the time it takes for a minority
carrier to cross the quasi-neutral base region.
iB 
iC 
QB
B
QB
  B  b dc t
t
EE130/230M Spring 2013
Lecture 26, Slide 19
Built-in Base E-Field to Reducet
The base transit time can be reduced by building into the base
an electric field that aids the flow of minority carriers.
1. Fixed EGB , NB decreases from emitter to collector:
E
B
-
C
Ec
Ef
Ev
2. Fixed NB , EGB decreases from emitter to collector:
E
-
B
C
Ec
Ef
Ev
EE130/230M Spring 2013
Lecture 26, Slide 20
E
EXAMPLE: Drift Transistor
• Given an npn BJT with W=0.1m and NB=1017cm-3
(n=800cm2/Vs), find t and estimate the base electric field
required to reduce t

2
5

2
W
10 cm
t 

 2 ps
2
2 DB 20.026V  800cm / V  s
W
v
drift


W
 n



t
10 5 cm


 6kV / cm
2
12
 n t 800cm / V  s 2 10 s
W
EE130/230M Spring 2013


Lecture 26, Slide 21
