SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

180 CHAPTER 4. JUNCTIONS IN SEMICONDUCTORS:P-NDIODES

Jp

Jn0 Jp0

Jn

JTotal

wa

Figure 4.20: Majority and minority currents in a reverse-biasedp−i−njunction

Defining a multiplication factor,M,

M=

JTotal

Jp 0 +Jn 0

=

JTotal

Js

(4.7.13)

the equation reduces to:

1 −

1

M

=

∫wa

0

αdx (4.7.14)

or

M=

[

1 −

∫wa

0

αdx

]− 1

(4.7.15)

Breakdown is defined as the case whereJTotal→∞orM→∞. This condition is achieved
when

1 −

∫wa

0

αdx→ 0 (4.7.16)

or ∫wa

0

αdx→ 1 (4.7.17)

We recognize thatαis af(E)in general. In the case of a constantα, the breakdown condition
reduces to
α·wa→ 1

which represents the case of every electron (hole) injected into the high field region generating
an electron-hole pair before exiting. This process is self-sustaining.

4.7.1 Reverse Bias: Zener Breakdown ......................

Impact ionization or avalanche breakdown is one mechanism for breakdown in diodes. There
is another one that can be important for narrow gap diodes or heavily doped diodes. This mech-
anism is due to the quantum-mechanical process of tunneling. The tunneling process, allows