Reverse-Biased PN Junctions

Theory of reverse pn junction
o Reverse saturation current, IS
o IS is independent of voltage
o However, experimental results are as shown in the IV graph below
o Threshold voltage Vth  Eg / e
o Reverse breakdown voltage typically is 5 V to 500 V, depending on design
o  New effects need to be added to the theory to explain the breakdown effect
o Reverse breakdown is not destructive (does not destroy the device), if the diode
power dissipated in the device ( P  VB I ) is small

Next, we discuss the depletion layer width, WD, and electric field, E, in a reverse-biased
pn junction
o Depletion layer width. Recall:
WD (V ) 
2  (VD  V )
e
 1
1 



N
N
A
D


… equation shows that WD is small for high doping
Chapter 13 – page 1
(1)
o Maximum electric field. Recall:
Ε max  
e
N A x p0

(2)
Also recall:
x p0 
ND
WD
NA  ND
(3)
It follows from Eqns. (1) – (3) that
Ε max
 
 1
e
1
2 (VD  V ) 


ND
 NA
… Ε max increases for reverse bias
Chapter 13 – page 2



1
(4)
Zener effect (tunneling breakdown)

“Tunneling” is a quantum mechanical effect
o Classical mechanics versus quantum mechanics:

A soccer ball with energy Eball  Epot, barrier
cannot get from one
potential well to another one.

An electron with kinetic energy Eelectron  Epot, barrier can tunnel from
one potential well to another one.
If Ekin, ball  Epot, ball  Epot, wall , Then the ball will stay in the
First well and cannot transfer to the second well.
o Basis for quantum mechanical tunneling is Heisenberg’s uncertainty principle
E t  h
(5)
o If product of energy barrier height (E) and time required for tunneling (t) is
sufficiently small, that is smaller than Planck’s constant h, then tunneling will
occur.
 Tunnel barrier height E must be low for tunneling to occur.
o If particle velocity = constant, then x  t .
 Tunnel barrier thickness x must be thin for tunneling to occur.
o Next, we apply this knowledge to a reverse-biased pn junction
Chapter 13 – page 3
o Tunneling breakdown requires a large amount of filled states and a large amount
of empty states separated by a potential barrier. Potential barrier must be low
and narrow.
 1
1
o Recall: WD  

 NA ND
o Tunnel distance
x 
1/ 2



 Heavy doping makes potential barrier narrow
1
E max

1
 V 1/ 2
o Tunneling breakdown will occur in lightly doped pn junctions at sufficiently high
reverse voltages. Tunneling breakdown is called Zener breakdown. Such diodes
are called Zener diodes. Typical Zener voltages = 5 – 20 V
Chapter 13 – page 4
Avalanche breakdown

Physical basis: Impact ionization at high electric fields. Generation of electron-hole pairs
by impact ionization.
o During impact ionization a rapidly propagating electrons hits the electron shell of
an atom and “kicks” an electron out of its orbit thereby ionizing the atom
o The free carriers created this way will create further free carriers by impact
ionization  carrier multiplication  higher current
o Band diagram:
o Classical analogue: Snow avalanche … chain reaction
o Avalanche breakdown occurs for …

Large depletion layer thicknesses WD

High electric fields
Note that
WD
 VD  V 1 / 2  (V )1 / 2
E max  VD  V 1 / 2  (V )1 / 2
Also note that for high reverse voltages, it is VD  V 1 / 2  V
Chapter 13 – page 5

Exercise:
o How would one design Zener diodes?
 Highly doped diodes
o How would one design diodes with a high breakdown voltage?
 Lowly doped pn junctions
Chapter 13 – page 6