Q.1 Describe insulator, conductor and
semiconductor on the basis of band theory.
(AKTU. 2005 - 06, 2010 - 11)
Ans. Insulators, Metals and Semiconductors on the
Basis of Band Gap: -
Far any given material, the forbidden energy-gap may
be large, small or non-existent. Thus, the difference between insulators,
metals and semiconductors is largely concerned with the relative widths of the
forbidden energy gaps. In this article, we shall discuss the electrical
properties of insulators, metals and semiconductors on the basis of band gap or
forbidden energy gap.
Insulators: -
In case of insulators, there is generally no electron in the conduction
band and the valence band is filled. Figure (a) shows the energy band diagram
of insulators. It may be observed from energy band diagram that there is a wide
gap between valence and conduction bands (forbidden energy gap). It is
generally 5 eV or more. Due to this wide gap, it is almost impossible for an
electron to cross the gap to go from valence band to conduction band. At room
temperature, the valence electrons of an insulator can not have so much energy
that it is able to jump to the conduction band. Due to this fact, the
insulators are not able to conduct electric current. This means that the
insulators have very high resistivity or extremely low conductivity at room
temperature. But an insulator may conduct if its temperature is very high or if
a very high voltage is applied across it. This is also known as the breakdown
of the insulators.
Metals or
Conductors: -
Figure (b) shows the energy band diagram of metals. It may be observed
that forbidden energy gap or energy gap between valence and conduction bands is
zero. In fact, the valence and conduction bands overlap each other. In a metal,
the valence band energies and conduction band energies are same. The orbits in
the conduction band are very large. An electron in the conduction band
experiences almost negligible nuclear attraction. Hence it is very easy for a
valence band electron to become a conduction band electron. It means that a
metal consists of a large number of free electrons without supplying any
external energy. Because of this fact, a metal works as a very good conductor.
Semiconductors: -
Figure (c)
shows the energy band diagram of a semiconductor. It may be observed that
forbidden energy gap EG is not very wide for semiconductors. It is
0.72 eV for germanium and 1.12 eV for silicon. At 0 K, the semiconductors
behave as insulators because there is no free electron to conduct in the
conduction band. However, in semiconductor, an electron can be lifted from the
valence band to the conduction band by imparting some amount of energy to it.
This energy must be more than energy gap EG. If the energy imparted to the electron is less than
EG, it cannot be lifted from
valence band to conduction band since no permissible energy levels exist
between the two bands. Room temperature provides the sufficient amount of
energy to lift electrons from the valence band to the conduction band. Some
electrons jump to conducton band. Hence at room temperature, semiconductors are
able to conduct some electric current. If
temperature is further raised above room temperature, more and more
valence electrons acquire energy and cross the energy to go to conduction band.
Hence semiconductors have negative temperature coefficient of resistance.
Q.2. Write
short note on fermi energy level.
Ans. Fermi Energy Level :-
The fermi
energy level, corresponds to the highest
filled energy level at 0 K. The free electrons occupy energies upto at 0 K. When the temperature goes up above 0
K, some lower energy electrons at energy E (E < ) move up to higher energy
levels E > EF. This motion of electrons under an applied electric field occurs
only when electrons are located in partially filled energy bands. Fermi energy
level of a metal can be determined by
where n is number of free electrons per unit volume of a metal, and rE is an energy density constant whose value is 6.821027 / m3 (eV)3/2. Number of free electrons in some metals are given in table.
where n is number of free electrons per unit volume of a metal, and rE is an energy density constant whose value is 6.821027 / m3 (eV)3/2. Number of free electrons in some metals are given in table.
