SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

6.6. SECONDARY EFFECTS IN REAL DEVICES 281

(b)

(a)

n - E p+ - B n- - C n+

Wbn

ΔWbn

VBC+ΔVBC

VBC

IC

VA

ideal

characteristics

Figure 6.21: (a) Slope of the electron profile in the base increases whenVBCis increased,
resulting in an increase inIC. (b) Device dcI-Vcharacteristics when Early Effect is accounted
for.

Using the Moll-Ross relationship in equation 6.5.22, the variation ofICwith respect toVBC
can be written as

∂IC

∂VBC

= −eDnn^2 iAEexp

(

eVBE

kBT

)

·

∂

∂x

(

1

∫Wbn

0 p(x)dx

)

(6.6.15)

=+eDnn^2 iAEexp

(

eVBE

kBT

)

·

p(Wbn)

[∫W

bn

0 p(x)dx

] 2

∂(Wbn)

∂VBC

(6.6.16)

Collecting terms, we can simplify this expression to

∂IC

∂VBC

=−IC

[

p(Wbn)·

1

∫Wbn

0 p(x)dx

·

∂Wbn

∂VBC

]

=−

IC

VA

=

IC

|VA|

(6.6.17)