6.6. SECONDARY EFFECTS IN REAL DEVICES 287
The slope of theJCvs.VCEcurve is then
dJC
dVCE
∼= ΔJC
ΔVCE
∼=^80.^35 −^75.^8
4
Acm−^2 V−^1
We define the Early voltageVAthrough the relation
dJC
dVCE
=
JC
VCE+VA
Equating the two relations, we get
VA∼= 64 .9V
Example 6.3Consider anpnSi-BJT at 300 K with the following parameters:
Nde =10^18 cm−^3
Nab =10^17 cm−^3
Ndc =5× 1016 cm−^3
Db =30.0cm^2 s−^1
Lb =15. 0 μm
De =10.0cm^2 s−^1
Le =5. 0 μm
(i) Calculate the maximum base width,Wb, that will allow a current gainβof 100 when
the EBJ is forward biased at 1.0 V and the BCJ is reverse biased at 5.0 V.
(ii) Describe two advantages and two disadvantages of making the base smaller.
Since the base width is much smaller than the base diffusion length, we have for the
emitter and collector current
IE=
[
eADbnb 0
Wbn
+
eADepe 0
Le
][
exp(
eVBE
kBT
)− 1
]
IC=
[
eADbnb 0
Wbn
][
exp(
eVBE
kBT
)− 1
]
The base current is the difference of these and the current gainβis
β=
IC
IB
=
Dbnb 0 Le
Depe 0 Wbn
= 100
This gives forWbn
Wbn=1. 5 × 10 −^4 cm
