EE130/230A
Discussion 14
Peng Zheng
1
“Game Plan” for I-V Derivation
• Solve the minority-carrier diffusion equation in each quasineutral region to obtain excess minority-carrier profiles
– different set of boundary conditions for each region
• Find minority-carrier diffusion currents at depletion region edges
dnE
E dx"
x"0
I En  qAD
dnC
C dx '
x ' 0
I Cn  qAD
dp B
B dx
x 0
I Ep  qAD
dp B
B dx
x W
I Cp  qAD
• Add hole & electron components together  terminal currents
EE130/230A Fall 2013
Lecture 26, Slide 2
BJT Terminal Currents
• We know:
I En  qA
DE
LE
I Ep  qA
DB
LB
I Cp  qA
DB
LB
I Cn  qA
nE 0 (e qVEB / kT  1)
pB0
p
DC
LC


1
B 0 sinh(W / LB )
nC 0 (e
qVCB / kT
• Therefore:

 qA
I E  qA
IC
DE
LE
nE 0 
DB
LB
EE130/230A Fall 2013
DB
LB


qVCB / kT
qVEB / kT
1
(
e

1
)

e
1
sinh(W / LB )
sinh(W / LB )
cosh(W / LB )
(e
qVEB / kT
1) 

e
qVCB / kT

1
 1)

pB 0 sinh(W / LBB )) (eqVEB / kT  1) 
cosh(W / L
cosh(W / LB )
sinh(W / LB )
pB0 sinh(W1 / LB ) (eqVEB / kT 1) 

DC
LC
Lecture 26, Slide 3

DB
LB


pB 0 sinh(W1 / LB ) eqVCB / kT  1
nC 0  DLBB pB 0
cosh(W / LB )
sinh(W / LB )
e
qVCB / kT

1
BJT with Narrow Base
• In practice, we make W << LB to achieve high current gain.
Then, since
sinh     for   1
cosh    1 
2
for   1
2
we have:
pB ( x)  pB 0 (e qVEB / kT  1)1  Wx 
 pB 0 (e qVCB / kT  1)Wx 
EE130/230A Fall 2013
Lecture 26, Slide 4
R. F. Pierret, Semiconductor Device Fundamentals, Fig. 11.2
Ebers-Moll Model
increasing
(npn) or VEC (pnp)
C. C. Hu, Modern Semiconductor Devices for Integrated Circuits, Figure 8-2
The Ebers-Moll model is a large-signal equivalent circuit which
describes both the active and saturation regions of BJT operation.
• Use this model to calculate IB and IC given VBE and VBC
EE130/230A Fall 2013
Lecture 26, Slide 5

 qA
I E  qA
DE
LE
IC
DB
LB
nE 0 
DB
LB
1
B 0 sinh(W / LB )
p

pB 0 sinh(W / LB ) (eqVEB / kT  1) 
cosh(W / LB )
(e
qVEB / kT
 1) 

DC
LC

nC 0 
If only VEB is applied (VCB = 0):
DB
LB
DB
LB

e

 1
pB 0 sinh(W1 / LB ) eqVCB / kT  1
cosh(W / LB )
pB 0 sinh(W / LB )
qVCB / kT
V EB
V CB
I E  I F 0 ( e qVEB / kT  1)
IB
I C   F I F 0 ( e qVEB / kT  1)
I B  1   F I F 0 ( e qVEB / kT  1)
If only VCB is applied (VEB = 0): :
I C   I R 0 (e qVCB / kT  1)
I E   R I R 0 (e qVCB / kT  1)
I B  I R 0 (1   R )(e
EE130/230A Fall 2013
qVCB / kT
 1)
E
B
C
IC
aR : reverse common base gain
aF : forward common base gain
Reciprocity relationship:
DB
pB 0
 F I F 0   R I R 0  qA
LB sinh( W / LB )
Lecture 26, Slide 6
In the general case, both VEB and VCB are non-zero:
I C   F I F 0 (e qVEB / kT  1)  I R 0 (e qVCB / kT  1)
IC: C-B diode current + fraction of E-B diode current that makes it to the C-B junction
I E  I F 0 (e qVEB / kT  1)   R I R 0 (e qVCB / kT  1)
IE: E-B diode current + fraction of C-B diode current that makes it to the E-B junction
Large-signal equivalent circuit for a pnp BJT
R. F. Pierret, Semiconductor Device Fundamentals, Fig. 11.3
EE130/230A Fall 2013
Lecture 26, Slide 7
Summary: BJT Performance Requirements
• High gain (bdc >> 1)
 One-sided emitter junction, so emitter efficiency g  1
• Emitter doped much more heavily than base (NE >> NB)
 Narrow base, so base transport factor T  1
• Quasi-neutral base width << minority-carrier diffusion length (W << LB)
• IC determined only by IB (IC  function of VCE,VCB)
 One-sided collector junction, so quasi-neutral base width W does
not change drastically with changes in VCE (VCB)
• Based doped more heavily than collector (NB > NC)
(W = WB – xnEB – xnCB for PNP BJT)
EE130/230A Fall 2013
Lecture 26, Slide 8
Questions regarding the MOSFET design project?
Good luck to Quiz#6!
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