SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

330 CHAPTER 7. TEMPORAL RESPONSE OF DIODES AND BIPOLAR TRANSISTORS

(a)

ve(x)

wd,BC

x

(b)

|eΔn(x)|

wd,BC

x

ΔQC

ΔQ'C

Figure 7.12: (a) Arbitrary velocity profileve(x)in the base-collector depletion region. (b) In-
jected chargeΔn(x)corresponding to this velocity profile, along with the image charges at the
depletion edges.AE

∫wd,BC

0 |eΔn(x)|dx=ΔQC+ΔQ

′

C(charge neutrality)

Solving fordE+(x)and using equation 7.5.16 to substitute forΔn(x)gives us

dE+(x)=

(

1 −

x

wC

)

ΔIC

AEve(x)

dx (7.5.22)

Substituting equation 7.5.17 into the equation above and integrating both sides, we can now
solve forΔQC.

d(ΔQC)=

(

1 −

x

wC

)

ΔIC

ve(x)

dx (7.5.23)

ΔQC=ΔIC

∫wC

0

(

1 −

x

wC

)

1

ve(x)

dx (7.5.24)