EE 203
1. In the BJT current derivation in class, we did a “quasi-ideal” treatment of the base. Now we
will derive the same expressions without making this approximation. The treatment of the
emitter and collector remains unchanged.
(a) Show that the minority carrier distribution in the base is
() ()
()
nB
nB
B
nB
nB
BB LW
Lx
Wn
LW
L
xW
nxn /sinh
/sinh
)(
/sinh
sinh
)0()( ∆+
−
∆=∆
(b) Calculate
x
n
qDI B
nBEn ∂
∆∂
=)0( and
x
Wn
qDI B
nBCn ∂
∆∂
=)( .
(c) Show that in the forward active region, the base transport factor,
()
nBEnCnTLWII cosh/1/ ==
α
. For W/LnB << 1, derive the expression found in class.
(d) Show that in the forward active region, the emitter injection efficiency,
)/cosh(
)/sinh(
1
1
nBDEpEnB
nBABnBpE
EpEn
En
LWNLD
LWNLD
II
I
+
=
+
=
γ
.
For W/LnB << 1, derive the expression found in class.
2. At VCE = 0, the family of IC vs. VCE curves seen on a curve tracer do not pass through the
origin.
(a) Using the Ebers Moll model, write an expression for Ic in terms of the Ebers Moll parameters
and VBE for VCE = 0.
(b) For a n+/p/n- BJT, taking into account the relative magnitudes of the Ebers Moll parameters,
sketch the curves at VCE = 0.
3. Suppose we wish to measure the I-V characteristics of the E-B junction of a n+ / p / n- BJT.
Does it matter whether we leave the collector open or shorted to the base? Use the Ebers Moll
model to prove your answer.
