SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

182 CHAPTER 4. JUNCTIONS IN SEMICONDUCTORS:P-NDIODES

Ec

Ev

Ec

Ev

E

Eg

–x 1 0 X

Potential energy

(a)

(b)

Forbidden gap

–x 2

EFp

EFn

Figure 4.22: (a) A schematic showing the band diagram for a reverse-biasedp-njunction along
with how an electron in the valence band can tunnel into an unoccupied state in the conduction
band.(b) The potential barrier seen by the electron during the tunneling process.

Zener breakdown), the current for reverse bias voltages greater thanVzis

I=

|V−Vz|

RL

(4.7.19)

Example 4.4A siliconp+ndiode has a doping ofNa=10^19 cm−^3 ,Nd=10^16 cm−^3.

Calculate the 300 K breakdown voltage of this diode. If a diode with the same/Ndvalue

were to be made from diamond, calculate the breakdown voltage.

The critical fields of silicon and diamond are (at a doping of 1016 cm−^3 )∼ 4 × 105 V/cm

and 107 V/cm. The breakdown voltage is

VBD(Si)=

(Ecrit)^2

2 eNd

=

(11.9)(8. 85 × 10 −^14 F/cm)(4× 105 V/cm)^2

2(1. 6 × 10 −^19 C)(10^16 cm−^3 )

=51.7V