PHYSICS
UNIT - 2
Chapter 4 : SEMICONDUCTORS
BAND THEORY OF SOLIDS
In an isolated atom there are discrete energy levels in which the electrons can exist. However in
solids, in which the atoms are very close to each other, due to interatomic interactions the
electronic energy levels form nearly continuous bands. These are called energy bands.
The highest energy band that is completely filled with electrons is known as a valence band.
The next available band above the valence band is known as a conduction band.
The separation between the valence band and the conduction band is known as energy gap (Eg).
A material can conduct electric current only if it has electrons in the conduction band.
CLASSIFICATION OF SOLIDS BASED ON BAND STRUCTURE
a) Conductors: In conductors the valence band
and the conduction band overlap (Fig. a). As
such, there is no energy gap. (Eg = 0). Thus, the
conduction band always has electrons in it (even
at 0°K). Hence, on application of electric
potential a large current (in Amperes) flows
through conductors.
Example: Copper, Aluminium, Gold, Silver
b) Insulators: In insulators, the conduction band
is completely empty. There is a large energy gap
between the valence band and the conduction
band. (Eg > 3eV) (Fig. b). To take electrons from
valence band to conduction band huge amount
of energy is required. Therefore, under normal
conditions, an insulator does not conduct electric
current.
Example: Plastic, wood, paper, rubber
Note: If sufficiently high voltage (energy) is
supplied to an insulator it breaks down and
conducts current.
c) Semiconductors: In semiconductors, at 0°K,
the conduction band is completely empty. Thus,
a semiconductor will not conduct current and
behave like an insulator at 0°K. The energy gap
between the valence band and the conduction
band is small (Eg < 2eV) (Fig c). Thus, at room
temperature, the surrounding energy is sufficient to overcome the energy gap and take some
electrons from valence band to conduction band. Hence, at room temperature, on application of
electric potential a small current (in milliamperes) flows through a semiconductor.
Example: Silicon, Germanium, Selenium, Gallium Arsenide (GaAs)
Note: As the temperature is raised, more and more electrons from valence band are taken to the
conduction band. Hence the current in a semiconductor increases with temperature.
Semiconductors Prof. Harison Cota, Don Bosco College of Engineering, Fatorda Page 1
, DRIFT CURRENT AND DRIFT VELOCITY (vd)
When an electric potential is applied across a
semiconductor, the free electrons start
moving (drifting) towards the positive
terminal, whereas holes move towards the
negative terminal as shown in the figure. This
movement of free charge carriers (electrons
and holes) produces a current in the
semiconductor called as Drift Current.
The average velocity with which the free
charge carriers drift through the
semiconductor when an electric potential is
applied across it is called Drift Velocity (denoted by 𝒗𝒅 ).
Mobility (𝝁)
The ratio of the drift velocity of the free charge carriers to the electric field applied is defined as
the mobility of charge carriers. It is denoted as 𝝁.
𝑣𝑑
Thus, 𝜇 = where ‘E’ is the applied electric field
𝐸
SI units of mobility: m2/V.s
CONDUCTIVITY OF CHARGE CARRIERS (𝝈)
Consider a rectangular block of semiconductor of length
‘𝐿’ and area of cross-section ‘𝐴’. Let ‘𝑛’ be the
concentration of free electrons (or holes) available in it.
Total number of free electrons in the semiconductor,
𝑁 = 𝑛𝐴𝐿
Total free charge present in it, 𝑄 = 𝑁. 𝑒 = 𝑛 𝑒 𝐴 𝐿
Let a potential difference ‘𝑉’ be applied across the
𝑉
semiconductor so that an electric field, 𝐸 = 𝐿
will be set up in it.
The resulting drift current through the conductor will be,
𝑄 𝑛𝑒𝐴𝐿
𝐼= =
𝑡 𝑡
𝐿
= 𝑛 𝑒 𝐴 𝑣𝑑 (since 𝑡 = 𝑣𝑑 = drift velocity)
The current density ‘J’ is given by,
𝐼 𝑛 𝑒 𝐴 𝑣𝑑
𝐽=𝐴= = 𝑛 𝑒 𝑣𝑑 ……..eqn.1
𝐴
From Ohm’s Law, we have
𝑉 𝑉𝐴 𝜌𝐿
𝐼=𝑅= (since 𝑅 = , where 𝜌 is the resistivity)
𝜌𝐿 𝐴
1 𝑉
=𝜎𝐴𝐸 (since 𝜌 = 𝜎, and 𝐿 = 𝐸)
𝐼 𝜎𝐴𝐸
Current density, 𝐽 = 𝐴 = =𝜎𝐸 ……..eqn.2
𝐴
From eqn.1 and eqn.2 we have,
𝜎 𝐸 = 𝑛 𝑒 𝑣𝑑
𝑛 𝑒 𝑣𝑑 𝑣𝑑
⇒ 𝜎= =𝑛𝑒𝜇 (since = 𝜇 = mobility of charge carriers)
𝐸 𝐸
Semiconductors Prof. Harison Cota, Don Bosco College of Engineering, Fatorda Page 2
UNIT - 2
Chapter 4 : SEMICONDUCTORS
BAND THEORY OF SOLIDS
In an isolated atom there are discrete energy levels in which the electrons can exist. However in
solids, in which the atoms are very close to each other, due to interatomic interactions the
electronic energy levels form nearly continuous bands. These are called energy bands.
The highest energy band that is completely filled with electrons is known as a valence band.
The next available band above the valence band is known as a conduction band.
The separation between the valence band and the conduction band is known as energy gap (Eg).
A material can conduct electric current only if it has electrons in the conduction band.
CLASSIFICATION OF SOLIDS BASED ON BAND STRUCTURE
a) Conductors: In conductors the valence band
and the conduction band overlap (Fig. a). As
such, there is no energy gap. (Eg = 0). Thus, the
conduction band always has electrons in it (even
at 0°K). Hence, on application of electric
potential a large current (in Amperes) flows
through conductors.
Example: Copper, Aluminium, Gold, Silver
b) Insulators: In insulators, the conduction band
is completely empty. There is a large energy gap
between the valence band and the conduction
band. (Eg > 3eV) (Fig. b). To take electrons from
valence band to conduction band huge amount
of energy is required. Therefore, under normal
conditions, an insulator does not conduct electric
current.
Example: Plastic, wood, paper, rubber
Note: If sufficiently high voltage (energy) is
supplied to an insulator it breaks down and
conducts current.
c) Semiconductors: In semiconductors, at 0°K,
the conduction band is completely empty. Thus,
a semiconductor will not conduct current and
behave like an insulator at 0°K. The energy gap
between the valence band and the conduction
band is small (Eg < 2eV) (Fig c). Thus, at room
temperature, the surrounding energy is sufficient to overcome the energy gap and take some
electrons from valence band to conduction band. Hence, at room temperature, on application of
electric potential a small current (in milliamperes) flows through a semiconductor.
Example: Silicon, Germanium, Selenium, Gallium Arsenide (GaAs)
Note: As the temperature is raised, more and more electrons from valence band are taken to the
conduction band. Hence the current in a semiconductor increases with temperature.
Semiconductors Prof. Harison Cota, Don Bosco College of Engineering, Fatorda Page 1
, DRIFT CURRENT AND DRIFT VELOCITY (vd)
When an electric potential is applied across a
semiconductor, the free electrons start
moving (drifting) towards the positive
terminal, whereas holes move towards the
negative terminal as shown in the figure. This
movement of free charge carriers (electrons
and holes) produces a current in the
semiconductor called as Drift Current.
The average velocity with which the free
charge carriers drift through the
semiconductor when an electric potential is
applied across it is called Drift Velocity (denoted by 𝒗𝒅 ).
Mobility (𝝁)
The ratio of the drift velocity of the free charge carriers to the electric field applied is defined as
the mobility of charge carriers. It is denoted as 𝝁.
𝑣𝑑
Thus, 𝜇 = where ‘E’ is the applied electric field
𝐸
SI units of mobility: m2/V.s
CONDUCTIVITY OF CHARGE CARRIERS (𝝈)
Consider a rectangular block of semiconductor of length
‘𝐿’ and area of cross-section ‘𝐴’. Let ‘𝑛’ be the
concentration of free electrons (or holes) available in it.
Total number of free electrons in the semiconductor,
𝑁 = 𝑛𝐴𝐿
Total free charge present in it, 𝑄 = 𝑁. 𝑒 = 𝑛 𝑒 𝐴 𝐿
Let a potential difference ‘𝑉’ be applied across the
𝑉
semiconductor so that an electric field, 𝐸 = 𝐿
will be set up in it.
The resulting drift current through the conductor will be,
𝑄 𝑛𝑒𝐴𝐿
𝐼= =
𝑡 𝑡
𝐿
= 𝑛 𝑒 𝐴 𝑣𝑑 (since 𝑡 = 𝑣𝑑 = drift velocity)
The current density ‘J’ is given by,
𝐼 𝑛 𝑒 𝐴 𝑣𝑑
𝐽=𝐴= = 𝑛 𝑒 𝑣𝑑 ……..eqn.1
𝐴
From Ohm’s Law, we have
𝑉 𝑉𝐴 𝜌𝐿
𝐼=𝑅= (since 𝑅 = , where 𝜌 is the resistivity)
𝜌𝐿 𝐴
1 𝑉
=𝜎𝐴𝐸 (since 𝜌 = 𝜎, and 𝐿 = 𝐸)
𝐼 𝜎𝐴𝐸
Current density, 𝐽 = 𝐴 = =𝜎𝐸 ……..eqn.2
𝐴
From eqn.1 and eqn.2 we have,
𝜎 𝐸 = 𝑛 𝑒 𝑣𝑑
𝑛 𝑒 𝑣𝑑 𝑣𝑑
⇒ 𝜎= =𝑛𝑒𝜇 (since = 𝜇 = mobility of charge carriers)
𝐸 𝐸
Semiconductors Prof. Harison Cota, Don Bosco College of Engineering, Fatorda Page 2
