6.012 - Microelectronic Devices and Circuits
Lecture 7 - Bipolar Junction Transistors - Outline
• Announcements
First Hour Exam - Oct. 7, 7:30-9:30 pm; thru 10/2/09, PS #4
• Review/Diode model wrap-up
Exponential diode: iD(vAB) = IS (eqvAB/kT -1)
(holes)
(electrons)
with IS ≡ A q ni2 [(Dh/NDn wn*) + (De/NAp wp*)]
Observations: Saturation current, IS, goes down as doping levels go up
Injection is predominantly into more lightly doped side
Asymmetrical diodes: the action is on the lightly doped side
Diffusion charge stores; diffusion capacitance:
(Recitation topic)
Excess carriers in quasi-neutral region = Stored charge
• Bipolar junction transistor operation and modeling
Bipolar junction transistor structure
Qualitative description of operation: 1. Visualizing the carrier fluxes
2. The control function
3. Design objectives
Operation in forward active region, vBE > 0, vBC < 0: δE, δB, βF, IES
(using npn as the example)
Clif Fonstad, 10/1/09
Lecture 7 - Slide 1
Biased p-n junctions: current flow, cont.
The saturation current of three diode types:
IS's dependence on the relative sizes of w and Lmin
p’(x), n’(x)
p’(xn)
Short-base diode, wn << Lh, wp << Le:
n’(-xp)
x
#
-wp
-xp xn
wn
n 2i
Dh
qv AB / kT
J h (x n ) = q
e
-1
[
] %%
'
*
N Dn ( w n " x n )
Dh
De
2
, [e qv AB / kT -1]
+
$ iD = Aqn i )
2
n
De
)( N Dn ( w n " x n ) N Ap ( w p " x p ) ,+
J e (-x p ) = q i
e qv AB / kT -1] %
[
N Ap ( w p " x p )
%&
p’(x), n’(x)
p’(xn)
Long-base diode, wn >> Lh, wp >> Le:
n’(-xp)
"
-wp
-xp xn
wn
n 2i Dh qv AB / kT
J h (x n ) = q
e
-1] $
[
& D
$
N Dn Lh
De ) qv AB / kT
2
h
+
-1]
# iD = Aqn i (
+ [e
n 2i De qv AB / kT
N
L
N
L
' Dn h
Ap e *
J e (-x p ) = q
e
-1] $
[
$%
N Ap Le
!
General diode:
x
" D
De % qv AB / kT
h
iD = Aqn $
+
-1]
' [e
# N Dn w n,eff N Ap w p,eff &
2
i
!
Hole injection into n-side
Clif Fonstad, 10/1/09
!
Electron injection into p-side
Note : w n,eff " Lh tanh( w n - x n ), w p,eff " Le tanh( w p - x p )
Lecture 7 - Slide 2
Asymmetrically doped junctions: an important special case
Current flow impact/issues
A p+-n junction (NAp >> NDn):
" D
Dh
De % qv AB / kT
2
2
h
e qv AB / kT -1]
iD = Aqn i $
+
-1] " Aqn i
' [e
[
N Dn w n,eff
# N Dn w n,eff N Ap w p,eff &
Hole injection into n-side
!
An n+-p junction (NDn >> NAp):
" D
De % !qv AB / kT
De
2
h
iD = Aqn i $
+
-1] ( Aqn 2i
e qv AB / kT -1]
' [e
[
N Ap w p,eff
# N Dn w n,eff N Ap w p,eff &
Electron injection into p-side
!
Note that in both cases the minority carrier injection is predominately into
the lightly doped side.
Note also that it is the doping level of the more lightly doped junction that
determines the magnitude of the current, and as the doping level on the
lightly doped side decreases, the magnitude of the current increases.
Two very important and useful observations!!
Clif Fonstad, 10/1/09
Lecture 7 - Slide 3
Biased p-n junctions: excess minority carrier (diffusion) charge stores
Diffusion charge store, and diffusion capacitance:
Using example of asymmetrically doped p+-n diode
p’(x), n’(x)
p’(xn)
Charge stored
on n-side (holes
and electrons)
Note: Assuming
negligible charge
stored on p-side
n’(-xp)
-wp
-xp
x
xn
wn
Notice that the stored positive charge (the excess holes) and the
stored negative charge (the excess electrons) occupy the same
volume in space (between x = xn and x = wn)!
qA,DF (v AB ) = Aq[ p'(x n ) " p'(w n )]
!
[w n " x n ]
2
#
w n,eff
n i2 qv AB / kT
Aq
e
"1]
[
N Dn
2
The charge stored depends non-linearly on vAB. As we did in the
case of the depletion charge store, we define an incremental linear
equivalent diffusion capacitance, Cdf(VAB), as:
#qA,DF
Cdf (VAB ) "
#v AB
Clif Fonstad, 10/1/09
$
v AB =VAB
q2
n i2 qv AB / kT
A
w n,eff
e
2kT
N Dn
Lecture 7 - Slide 4
p’(x), n’(x)
Diffusion capacitance, cont.:
p’(xn)
Excess holes and
electrons stored
on the n-side
n’(-xp)
-wp
-xp
x
xn
wn
A very useful way to write the diffusion capacitance is in
terms of the bias current, ID:
ID " Aqn i2
Dh
Dh
e qVAB / kT #1] " Aqn i2
e qVAB / kT for VAB >> kT
[
N Dn w n,eff
N Dn w n,eff
To do this, first divide Cdf by ID to get:
q2
n i2 qVAB / kT
A
w n,eff
e
Cdf (VAB )
2kT
N Dn
"
Dh
ID (VAB )
Aqn i2
e qVAB / kT
N Dn w n,eff
!
Isolating Cdf, we have:
!
Clif Fonstad, 10/1/09
=
2
q w n,eff
2 kT Dh
2
w n,eff
q ID (VAB )
Cdf (VAB ) "
! 2 Dh
kT
* Notice that the area of the device, A, does not appear
explicitly in this expression. Only the total current!
!
Lecture 7 - Slide 5
Comparing charge stores; small-signal linear equivalent capacitors:
"
qA,PP = A v AB
d
Parallel plate capacitor
ρ(x)
qA
d/2
$qA,PP
C pp (VAB ) #
$v AB
x
-d/2
qB( = -qA)
Depletion region charge store
ρ(x)
qNDn
v AB =VAB
A"
d
qA,DP (v AB ) = "A 2q#Si [$ b " v AB ]
!
qB
-xp
=
N Ap N Dn
[N
Ap
+ N Dn ]
( = -QA)
x
xn
qA
Cdp (VAB ) = A
-qNAp
N Ap N Dn
q#Si
2[$ b " VAB ] [ N Ap + N Dn ]
=
A #Si
w(VAB )
QNR region diffusion charge store
p’(x), n’(x)
p’(xn)
!
qA, qB (=-qA)
Note: Approximate because we are
only accounting for the charge
store on the lightly doped side.
n’(-xp )
-wp
-xp
xn
qAB,DF (v AB ) " Aqn i2
x
wn
Cdf (VAB ) "
Clif Fonstad, 10/1/09
!
Dh
e qVAB / kT #1]
[
N Dn w n,eff
2
w n,eff
q ID (VAB )
2 Dh
kT
=
2
w n,eff
iD (v AB )
2 Dh
Lecture 7 - Slide 6
p-n diode:
large signal model including charge stores
A
qAB
IBS
Non-linear
resistive
element
B
qAB: Excess carriers on p-side +
excess carriers on n-side +
junction depletion charge.
Non-linear
capacitive
element
small signal linear equivalent circuit
a
Cd
gd
b
Clif Fonstad, 10/1/09
#iD
gd "
#v AB
v AB =VAB
#qAB
Cd (VAB ) "
#v AB
%
' 0
$ & qID
'
( kT
v AB =VAB
for
VAB < 0
for VAB >> kT /q
%
Cdp (VAB )
for
VAB < 0
$&
( Cdp (VAB ) + Cdf (VAB ) for VAB >> kT /q
Lecture 7 - Slide 7
!
Moving on to transistors!
Amplifiers/Inverters:
back to 6.002
V CC
V CC
RD
RC
D
RT
vT (t) =
V T + vt (t)
+
-
C
+
vIN
-
S
vOUT
An MOS amplifier
or inverter:
the transistor is an
n-channel MOSFET
Clif Fonstad, 10/1/09
RT
+
G
-
vT (t) =
V T + vt (t)
+
-
+
B
+
vIN
-
vOUT
E
-
A bipolar amplifier
or inverter:
the transistor is an
npn BJT
Lecture 7 - Slide 8
npn BJT: Connecting with the n-channel MOSFET from 6.002
A very similar behavior*, and very similar uses.
iD
MOSFET
D
Linear
iD or
Triode
+
iG
Saturation (FAR)
vDS
G+
iD ! K [vGS - V T(vBS)]2/2!
vGS
–
iC
BJT
C
–
S
Cutoff
+
vDS
iB
Saturation
vCE
B+
iC
i
B
vBE
–
–
E
FAR
iB ! IBSe qV BE /kT
vCE > 0.2 V
Cutoff
0.6 V
Input curve
Clif Fonstad, 10/1/09
vBE
Forward Active Region
iC ! !F iB
0.2 V
Cutoff
vCE
Output family
Lecture 7 - Slide 9
* At its output each device looks like a current source controlled by the input signal.
How do we make a BJT?
Basic Bipolar Junction Transistor (BJT) - cross-section
Base, B
Emitter, E
Al
p
SiO2
n+
n
Si
An npn BJT
Adapted from Fig. 8.1 in Text
Al
Collector, C
The heart of the device, and what we will model
Clif Fonstad, 10/1/09
How does it work?
Lecture 7 - Slide 10
Bipolar Junction Transistors: basic operation and modeling…
C
iC
C
iC
Reverse biased
vCB, the reverse bias on the collector-base junction, insures
collection of those electrons
injected across the E-B junction that reach the C-B junction as the collector current, iC
n
NDC
B
− E
iB
B
p
NAB
+
+
vBE
+
… how the base-emitter voltage, vBE, controls the collector current, iC
vCE
n+
vBE
NDE
−
E
iE
−
Forward biased
vBE, the bias on the emitter-base
junction, controls the injection
of electrons across the E-B
junction into the base and
toward the collector.
A good way to envision this is to think "carrier fluxes":
Clif Fonstad, 10/1/09
Next foil
Lecture 7 - Slide 11
C
iC
vCE
B
+
vBE
n
NDC
− E
iB
iB
p
NAB
+
B
The base
supplies
the small
hole flux
vBE
E
Hole flux
B
n+
NDE
−
Reverse biased
BC junction
collects electrons
coming across
the base from the
emitter
+
iB
C
iC
+
C
iC
+
Bipolar Junction Transistors: the carrier fluxes through an npn
Electron
flux
vBE
iE
−
−
E
iE
−
Forward biased
n+-p EB junction
emits electrons
into the base
towards the BC
junction
Our next task is to determine:
Given a structure, what are iE(vBE,vCE), iC(vBE,vCE), and iB(vBE,vCE)?
Clif Fonstad, 10/1/09
Lecture 7 - Slide 12
Bipolar Junction Transistors: basic operation and modeling…
… how the base-emitter voltage, vBE, controls the collector current, iC
vCE
n
NDE
E
vBE
p
NAB
+B
-wE
−
−
Excess Carriers:
iiE
E
+
n
NDC
C
iC
iB
wB
0
p!, n!
Electron (ni2/NAB)(e qvBE/kT - 1)
Electron
flux
2
qv
BE
/kT
(ni /NDE)(e
- 1)
flux
E
E−
−
0 (ohmic)
+
+
Clif Fonstad, 10/1/09
v
vBE
BE
0
B
B
Hole
Hole
fluxflux
-wE
0 (vBC = 0)
x
wB + wC
+
+
- iE
C
C
iiC
0 (ohmic)
C
x
wB
iiB
B
wB + wC
This is rigorous for vCB = 0, but
also very good when vCB > 0.
Lecture 7 - Slide 13
Bipolar Junction Transistors: basic operation and modeling…
… how the base-emitter voltage, vBE, controls the collector current, iC
vCE
n
NDE
E
vBE
p
NAB
+B
-wE
−
−
Excess Carriers:
iiE
E
+
n
NDC
C
iC
iB
wB
0
p!, n!
Electron (ni2/NAB)(e qvBE/kT - 1)
Electron
flux
2
qv
BE
/kT
(ni /NDE)(e
- 1)
flux
E
E−
−
0 (ohmic)
+
+
Clif Fonstad, 10/1/09
v
vBE
BE
0
B
B
Hole
Hole
fluxflux
-wE
0 (vBC = 0)
x
wB + wC
+
+
- iE
C
C
iiC
0 (ohmic)
C
x
wB
iiB
B
wB + wC
This is rigorous for vCB = 0, but
also very good when vCB > 0.
Lecture 7 - Slide 14
npn BJT: Forward active region operation, vBE > 0 and vBC ≤ 0
Excess Carriers:
p!, n!
(ni2/NAB)(e qvBE/kT - 1)
(ni2/NDE)(e qvBE/kT - 1)
0 (ohmic)
~ 0 (vBC < 0)
0 (ohmic)
x
-wE
0
wB
wB + wC
wB
wB + wC
ie, ih
Currents:
-wE
ihE [= !EieE]
0
x
–iC [= ieE (1 – !B )]
ieE
}
iE [= ieE + ieE = ieE (1 + !E)]
Clif Fonstad, 10/1/09
–iB [= ihE + !B ieE
= ieE (!E + !B )]
Lecture 7 - Slide 15
npn BJT: Approximate model for iE(vBE,vBC) and iC(vBE,vBC)
in forward active region, vBE>0, vBC<0
p!, n!
(ni2/NAB)(e qvBE/kT - 1)
(ni2/NDE)(e qvBE/kT - 1)
0 (ohmic)
~ 0 (vBC < 0)
0 (ohmic)
x
-wE
wB + wC
wB
0
The emitter current, iE
Begin with the good current, the electron current into the base, ieE:
ieE = "Aqn i2
De
e qVBE / kT "1]
[
N AB w B,eff
Next find the bad current, the hole current back into the emitter, ihE:
ihE = "Aqn i2
!
Dh
e qVBE / kT "1]
[
N DE w E ,eff
and write it as a fraction of ieE:
ihE =
Clif Fonstad, 10/1/09
!
N AB w B ,eff
Dh
ieE = "E ieE
De
N DE w E ,eff
We'll define δE on the next foil.
Lecture 7 - Slide 16
npn BJT: Approximate forward active region model, cont.
ie, ih
-wE
ihE [= !EieE]
iE [= ieE + ieE = ieE (1 + !E)]
wB
0
wB + wC
x
–iC [= ieE (1 – !B )]
ieE
}
–iB [= ihE + !B ieE = ieE (!E + !B )]
The emitter current, iE, cont.
In writing the last equation we introduced the emitter defect, δE:
"E #
w
ihE
D N
= h $ AB $ B ,eff
ieE
De N DE w E ,eff
To finish for now with the emitter current, we write it, iE, in terms
of the emitter electron current, ieE:
!
" ihE %
iE = ieE + ihE = $1+ ' ieE = (1+ (E ) ieE
# ieE &
Clif Fonstad, 10/1/09
Lecture 7 - Slide 17
!
npn BJT: Approximate forward active region model, cont.
ie, ih
-wE
wB
0
ihE [= !EieE]
wB + wC
x
–iC [= ieE (1 – !B )]
ieE
iE [= ieE + ieE = ieE (1 + !E)]
}
–iB [= ihE + !B ieE = ieE (!E + !B )]
The collector current, iC
The collector current is the electron current from the emitter, ieE,
minus the fraction that recombines in the base, δBieE:
iC = (1" #B ) ieE
To find the fraction that recombine, i.e. the base defect, δB, we
note that we can write the total recombination in the base, δBieE,
!
as:
wB
"B ieE = #Aq %
0
Clif Fonstad, 10/1/09
n'(x)
dx
$ eB
Lecture 7 - Slide 18
!
npn BJT: Approximate forward active region model, cont.
The base defect, δB
If the recombination in the base is small (as it is in a good BJT)
then the excess electron concentration will be nearly triangular
and we can say:
wB
"
0
n'(0)w B,eff
n'(x)dx #
2
wB
Thus
"B =
!
#A q %
0
n'(x)
dx
$ eB
ieE
and
ieE " # Aq DeB
n'(0)
w B,eff
n'(0)w B,eff
#Aq
2
w B2 ,eff
w B,eff
2$ eB
& !
=
=
2
n'(0)
2D
$
2
L
eB eB
eB
#A q DeB
w B,eff
The collector current, iC, cont.
Returning to the collector current, iC, we now want to relate it to
the total emitter current:
!
iC = "(1" #B ) ieE $
(1" #B ) i = "' i
% iC = "
F E
iE = (1+ #E ) ieE &
(1+ #E ) E
with " F #
Clif Fonstad, 10/1/09
!
(1$ %B )
(1+ %E )
Lecture 7 - Slide 19
npn BJT: Approximate forward active region model, cont.
So far...
We have:
# D
De & qVBE / kT
h
iE = " Aqn %%
+
"1]
(([e
$ N DE w E ,eff N AB w B ,eff '
# D
De &
qVBE / kT
2
h
= " IES [e
"1]
with IES = Aqn i %%
+
((
$ N DE w E ,eff N AB w B,eff '
…and we have:
1# &B )
iC
(
iC " iE :
iC = # $ F iE with $ F % #
=
iE
(1+ &E )
!
These relationships can be represented by a simple circuit model:
!
B iB
+
vBE
2
i
C
!FiF
or "FiB
iF
IES
– E
Note: iF = -iE.
Clif Fonstad, 10/1/09
iE = " iF
iC = # F iF
with iF = IES (1" e qv BE / kT )
with # F $ "
iC
(1" %B )
=
iE
(1+ %E )
iB = " iE " iC = (1" # F )iF
Looking at this circuit and these expressions,
it is clear that to make iB small and |iC| ≈ |iE|,
we must have αF ≈ 1. We look at this next.
!
Lecture 7 - Slide 20
C
iC
C
+
npn BJT: Approximate forward active region model, cont.
iC
iB
B
+
vBE
Reverse biased
BC junction
collects electrons
coming across
the base from the
emitter
− E
B
The base
supplies
the small
hole flux
B iB
+
vBE
Hole flux
–
+
iB
C
!FiF
or "FiB
iF
IES
n+-p
Forward biased
EB
junction emits electrons
into the base towards the
BC junction
Electron
flux
vBE
−
E
iE
−
E
iE = " iF = " IES (1" e qv BE / kT )
iC = # F iF
iB = " iE " iC = (1" # F )iF
Clif Fonstad, 10/1/09
Lecture 7 - Slide 21
npn BJT: What our model tells us about device design.
We have:
"F =
(1# $B )
(1+ $E )
and the defects, δE and δB, are given by:
!
"E
Dh N AB w B,eff
=
#
#
De N DE w E,eff
and
"B #
w B2 ,eff
2L2eB
We want αF to be as close to one as possible, and clearly
the smaller we can make the defects, the closer αF will be
!
! to one. Thus making the defects
small is the essence of
good BJT design:
Doping : npn with N DE >> N AB
w B,eff : very small
LeB : very large and >> w B,eff
Clif Fonstad, 10/1/09
Lecture 7 - Slide 22
!
npn BJT: Well designed structure (Large βF, small δE and dB)
δE and δB are small and αF is ≈ 1 when NDE >> NAB, wE << LhE, wB<<LeB
p!, n!
Excess Carriers:
(ni2/NAB)(e qvBE/kT - 1)
(ni2/NDE)(e qvBE/kT - 1)
0 (ohmic)
0 (vBC = 0)
0 (ohmic)
x
-wE
0
wB + wC
wB
wB + wC
ie, ih
Currents:
-wE
ihE [= !EieE]
iE [= ieE(1 + !E)]
Clif Fonstad, 10/1/09
wB
0
x
ieE
–iC [= ieE(1 – !B ) " ieE]
–iB [= iE – (– iC )
= ieE(!E + !B ) " ieE!E]
Lecture 7 - Slide 23
!
npn BJT,cont.: more observations about F.A.R. model
It is very common to think of iB, rather than iE, as the controlling
current in a BJT. In this case we write iC as depending on iB:
iE = " iF = "IES [e
iC = # F iF
iB = (1" # F )iF
qVBE / kT
with
"F #
*i = (1" # ) I [e qVBE / kT "1] = I [e qVBE / kT "1]
$
B
F ES
BS
"1]
&
& &
#F
iC =
iB = ) F iB
%(+
(1" # F )
& &
' &
iE = "iC " iB = () F + 1) iB
,
$F
(1% &B )
=
1% $ F (&E + &B )
and
IBS " (1# $ F ) IES =
IES
(% F + 1)
Two circuit models that fit this behavior are the following:
C
!
!FiB
B iB
+
IES
vBE
–
Clif Fonstad, 10/1/09
E
C
!
iB
B+
!FiB
Note:
"F =
IBS
vBE
–
E
#F
(# F + 1)
Lecture 7 - Slide 24
!
npn BJT: Equivalent FAR models
C
!FiF
B iBF
B iB
iF
IES
+
vBE
–
C
C
!FiB
iB
B+
+
vBE
IES
IES = Aqn i2 ( Dh N DE w E,eff + De N AB w B ,eff )
" F = # F (# F + 1)
IBS
vBE
– E
#F
"F =
(1$ # F )
E
!FiB
IBS
C
A useful model using a break-point diode:
!
+
vAB
–
Clif Fonstad, 10/1/09
A
iD
IS
B
!
+
≈ vAB
–
A
iD
VBE,ON
B
!
!FiB
iB
B
– E
= IES (" F + 1)
+
VBE,ON
vBE
–
This is a very useful model to use when
finding the bias point in a circuit.
E
Lecture 7 - Slide 25
npn BJT: The Ebers-Moll model
The forward model is what we use most, but adding the reverse model
we cover the entire range of possible operating conditions.
Forward:
B iBF
+
vBE
C
C
Reverse:
vBC
!FiF
ICS
iR
B
iF
IES
iBR
" D
De %
h
IES = Aqn $$
+
''
– E
N
w
N
w
# DE E,eff
AB B,eff &
(1) *B ) , + = (1) *B )
(F =
F
(*E + *B )
(1+ *E )
2
w B,eff
w B2 ,eff
Dh N AB w B ,eff
=
,
*B .
=
De N DE w E ,eff
2De / e
2L2e
αRiR
*E ,
ihE
ieE
E
–
vBC
!
Combined they form the
full Ebers-Moll model:
+
B+
iF
–
2
w B2 ,eff
w B,eff
*B .
=
2De / e
2L2e
!
!RiR
vBE
Clif Fonstad, 10/1/09
C
ICS
iR
!FiF
IES
" D
De %
h
ICS = Aqn $$
+
''
# N DC wC ,eff N AB w B,eff &
(1) *B ) , + = (1) *B )
(R =
R
(*C + *B )
(1+ *C )
w
i
D N
*C , hC = h - AB - B ,eff
ieC
De N DC wC ,eff
2
i
2
i
E
You are not responsible for this model.
Note: iF = -iE(vBE,0)
and iR = -iC(0,vBC).
Lecture 7 - Slide 26
npn BJT: The Gummel-Poon model
Another common model can be obtained from the Ebers-Moll model
is the Gummel-Poon model:
C
C
Forward:
!FiF
B iBF
iF
IES
+
vBE
–
=
B
iBF
+
vBE
E
IS "
Combined they form the
Gummel-Poon model:
Clif Fonstad, 10/1/09
C
!RiBR
iBR
E
E
= $ F IES = $ R ICS
• Aside from the historical interest, another
value this has for us in 6.012 is that it is an
interesting exercise to show that the two
forward circuits above are equivalent.
B
IS/!F
#F
#R
IES =
ICS
#
+
1
#
+
1
( F )
( R )
!
IS/!R
+
!FiBF
–
–
Reverse: vBC
vBC
–
IS/!R
iBR
iBF
IS/!F
+
B+
vBE
–
You even less responsible for this model.
C
!FiBF - !RiBR
E
Lecture 7 - Slide 27
6.012 - Microelectronic Devices and Circuits
Lecture 7 - Bipolar Junction Transistors - Summary
• Review/Junction diode model wrap-up
Refer to "Lecture 6- Summary" for a good overview
Diffusion capacitance: adds to depletion capacitance (p -n example)
+
In asym., short-base diodes: Cdf(VAB) ≈ (qID/kT)[(wn-xn)2/Dh]
(area doesn't enter expression!)
• Bipolar junction transistor operation and modeling
C
iC
Currents (forward active):
wB + wC
(npn example)
iE(vBE,0) = – IES (eqvBE/kT – 1)
iC(vBE,0) = – αF iE(vBE,0)
with αF ≡ [(1 – δB)/(1 + δE)]
n
––––––––––––––––––––––––––––––––––––––––––
iB
B
+
p
Electron
Flux
Hole
Flux
vBE
wB
0
-wE
E
Clif Fonstad, 10/1/09
iE
(ratio of hole to electron current across E-B junction)
Base defect, δB ≡ (wB2/2Le2)
n+
–
Emitter defect, δE ≡(DhNABwB*/DeNDEwE*)
(fraction of injected electrons recombining in base)
––––––––––––––––––––––––––––––––––––––––––
n!, p!
Also, iB(vBE,0) = [(dE + dB)/(1 + dE)] iE(vBE,0)
and, iC(vBE,0) = bF iB(vBE,0),
with bF º aF/(1 – aF) = [(1 – dB)/(dE + dB)]
Lecture 7 - Slide 28
MIT OpenCourseWare
http://ocw.mit.edu
6.012 Microelectronic Devices and Circuits
Fall 2009
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