SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

4.7. AVALANCHE BREAKDOWN IN AP-NJUNCTION 181

J

V

Total

Ideal

M ∞

Figure 4.21: Current-Voltage characteristics for ap−i−ndiode in avalanche breakdown
showing the ideal (non-avalanche) case as well as the limit whereMbecomes large.

electrons in the valence band to tunnel into the conduction band and vice versa. Electrons tun-
neling through the diode do not have to go over the barrier and as a result the diode reverse
current can increase dramatically.
To examine how tunneling occurs let us examine the band profile in a reverse-biasedp-n
junction. Assume that the diode is heavily doped so that the Fermi level on then-side and the
Fermi level on thep-side are in the conduction and valence bands, respectively. The heavy
doping ensures that electrons in the conduction band can tunnel into “available” empty states in
the valence band. A typical electron sees a potential barrier between pointsx 2 andx 1 ,asshown
in figure 4.22b. The tunneling probability is given under such conditions by

T≈exp

(

−

4

√

2 m∗Eg^3 /^2

3 eE

)

(4.7.18)

whereEgis the bandgap of the semiconductor,m∗is the reduced mass of the electron-hole
system, andEis the field.
There is a special class of diodes called Zener diodes where tunneling is exploited. The
depletion width can be controlled by the doping density. If the junction is made from heavily
doped materials, the Zener tunneling can start at a reverse bias ofVz, which could be as low as
a few tenths of a volt. The voltage across the junction is then clamped atVz, and the current is
controlled by the external circuit as shown in figure 4.23. This clamping property provides a very
useful application for the Zener diodes. IfVzis breakdown voltage (due to impact ionization or