SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

4.7. AVALANCHE BREAKDOWN IN AP-NJUNCTION 179

pin

Figure 4.19: Band diagram for ap−i−ndiode showing the avalanche ionization and mul-
tiplication process where an injected minority carrier causes generation of electron-hole pairs
through impact ionization. Multiple ionization events may be caused by a single carrier. The
star represents a collision which generates an electron-hole pair.

or
∂Jn
∂x

=α(Jp+Jn)=αJTotal (4.7.8)

Integrating over the length of the multiplication region,wa,weget
∫
dJn=JTotal

∫wa

0

αdx (4.7.9)

Jn(wa)−Jn(0) =JTotal

∫wa

0

αdx (4.7.10)

Recognizing
Jn(wa)=JT otal−Jp 0 (4.7.11)

andJ(0) =Jn 0 , one gets

JTotal−JP 0 −Jn 0 =JTotal

∫wa

0

αdx (4.7.12)