286 CHAPTER 6. BIPOLAR JUNCTION TRANSISTORS
The depletion width at the base-collector junction is shared between the base and the
collector region. The extent of depletion into the base side is given by
ΔWb=
{
2 s(Vbi+VCB)
e
(
Ndc
Nab(Nab+Ndc)
)} 1 / 2
The built-in voltageVbiis given by
Vbi =
kBT
e
ln
NabNdc
n^2 i
=(0.026(V))× n(1. 1 × 1012 )
=0.721 V
For an applied bias of 1 V, we get
ΔWb =
{
2 ×(8. 84 × 10 −^14 × 11 .9F/cm)(1.72 V)
(1. 6 × 10 −^19 C)
×
1
5. 5 × 1017 cm−^3
} 1 / 2
=6. 413 × 10 −^6 cm = 0. 064 μm
The neutral base width is thus
Wbn=0. 936 μm
When the collector-base voltage increases to 5 V, we get
ΔWb=0. 117 μm
The neutral base width is
Wbn=0. 883 μm
In the limit ofWbnLbwe have for the collector current density (using equation 6.3.17
with sinh(Wbn/Lb)∼Wbn/Lb)
JC=
eDbnbo
Wbn
exp
(
eVBE
kBT
)
where
nbo=
n^2 i
Nab
=
2. 25 × 1020
5 × 1016
=4. 5 × 103 cm−^3
For the base-collector bias of 1 V, we haveWbn=0. 936 μm. The collector current density
is then
JC =
(1. 6 × 10 −^19 C)×(20 cm^2 s−^1 )×(4. 5 × 103 cm−^3 )(4. 93 × 1011 )
(0. 936 × 10 −^4 cm)
=75.8A/cm^2
When the collector-base bias changes to 5 V, the current density becomes
JC=80.35 A/cm^2
