Solid State Physics
283
=
0
1/ 2
2
1
2
κε
+
e h
e
h
e n n
n n
V
(8.68)
The variation of C as V
–1/2
is the basis of the variable capacitance diodes
(varactors) which are used in frequency locking and frequency modulation
circuits.
8.5 SEMICONDUCTOR DEVICES
The special properties of semiconductors have led to a large number of important
applications. Here a few illustrative examples such as diodes, transistors, solar
cells and semiconductor lasers are discussed, and also the fabrication of these
devices is briefly described.
Semiconductor Diodes
The pn junction can be used as a rectifier, a voltage stabilizer and in high
frequency circuits.
Consider again the pn junction discussed in Sec. 8.4. Though the net current
across the junction is zero, the electrons and the holes diffuse across the boundary
but the flow in each direction is the same. The densities of electrons and holes
in the corresponding states (similarly located with respect to ε c or ε y ) on the two
sides are related by Boltzmann statistics,
( )
( )
e
e
n p
n n
= exp (– eV 0 /kT)
(8.69)
( )
( )
h
h
n n
n p
= exp (– eV 0 /kT)
(8.70)
where V 0 is the potential difference across the junction. It follows from these
relations that the product n e n h , of the total number of electrons and holes, has
the same value on the two sides.
To be specific, consider the flow of electrons across the boundary. Since
the motion of electrons from p to n is ‘downhill’, the rate of electron flow from
p to n is
I e (p → n) = c 1 n e (p)
(8.71)
where n e (p) is the total number of electrons in the conduction band on the
p-side. On the other hand the electrons flowing from n to p, face an ‘up-hill’
potential of V 0 and only those which have an energy of eV 0 will be able to cross
the boundary. The number of such electrons is proportional to n e (n) exp (– eV 0 kT),
so that
I e (n → p) = c 2 n e (n) exp (– eV 0 /kT)
(8.72)
283
=
0
1/ 2
2
1
2
κε
+
e h
e
h
e n n
n n
V
(8.68)
The variation of C as V
–1/2
is the basis of the variable capacitance diodes
(varactors) which are used in frequency locking and frequency modulation
circuits.
8.5 SEMICONDUCTOR DEVICES
The special properties of semiconductors have led to a large number of important
applications. Here a few illustrative examples such as diodes, transistors, solar
cells and semiconductor lasers are discussed, and also the fabrication of these
devices is briefly described.
Semiconductor Diodes
The pn junction can be used as a rectifier, a voltage stabilizer and in high
frequency circuits.
Consider again the pn junction discussed in Sec. 8.4. Though the net current
across the junction is zero, the electrons and the holes diffuse across the boundary
but the flow in each direction is the same. The densities of electrons and holes
in the corresponding states (similarly located with respect to ε c or ε y ) on the two
sides are related by Boltzmann statistics,
( )
( )
e
e
n p
n n
= exp (– eV 0 /kT)
(8.69)
( )
( )
h
h
n n
n p
= exp (– eV 0 /kT)
(8.70)
where V 0 is the potential difference across the junction. It follows from these
relations that the product n e n h , of the total number of electrons and holes, has
the same value on the two sides.
To be specific, consider the flow of electrons across the boundary. Since
the motion of electrons from p to n is ‘downhill’, the rate of electron flow from
p to n is
I e (p → n) = c 1 n e (p)
(8.71)
where n e (p) is the total number of electrons in the conduction band on the
p-side. On the other hand the electrons flowing from n to p, face an ‘up-hill’
potential of V 0 and only those which have an energy of eV 0 will be able to cross
the boundary. The number of such electrons is proportional to n e (n) exp (– eV 0 kT),
so that
I e (n → p) = c 2 n e (n) exp (– eV 0 /kT)
(8.72)