Free electron model that works well for metals do not apply for crystals. Free electrical
model gives us good insight into heat capacity, thermal conductivity, electron conductivity
& electrodynamics of metal; but it fails to answer other large question: distinction between
metals, semimetals, semiconductors & insulators; occurrence of positive values of Hall
coefficient & many detailed transport properties. The reason behind it is the periodicity of
the potential characterizing the crystal, whose value at any point is the result of
contributions from each atom. When atoms form crystals, presence of neighbouring atoms
does not affect the energy levels of inner shell electrons. However, the levels of outer shell
electrons are changed considerably, as the outer shell electrons are shared by more than
one atom in the crystal.
Quantum mechanics helps to find out the new energy levels of the outer electrons.
Coupling exists between the outer shell electrons of the atoms and is responsible for the
appearance of the band of closely spaced energy states, rather than widely separated
energy level as that of the isolated atoms. Regions in energy for which no wave like
electron orbital exists are called energy gaps or band gaps & results from the interaction of
the conduction electron wave with the ion cores of the crystal.
Each of the elements given above contains 2s electrons and 2p electron in the outer two
sub shells. If we ignore the inner shell levels, there are 2N electrons completely filling the
2N possible s levels all at same energy. Well known that p atomic sub shell has 6 possible
states, our crystal having widely spaced atoms (2N electrons), will fill only one third of
the 6N possible p states, all at the same level. Now if we decrease the interatomic spacing
of the crystal, each atom will experience an electric force from it’s neighbouring atoms.
This coupling between atoms gives rise to overlapping of atomic wave functions and
crystal becomes an electronic system which will obey Pauli exclusion principle. If
interatomic distance is decreased sufficiently, the total spread between the minimum and
maximum energy may be several electron volts, since N is very large (⋍1023cm-3),
although separation between levels is small.
Now each atom has given up 4 electrons to the band at this particular spacing; which no
longer belongs to orbit in s or p sub shell of an isolated atom, but rather they belong to the
crystal as a whole. The band occupied by these electrons is called valence band. Valence
band filed with 4N electrons is separated by a forbidden band (EG) from an empty band
consisting of 4N additional states. This upper vacant band is called conduction band.
METALS, INSULATORS & SEMICONDUCTORS
A very poor conductor of electricity is called insulator, whereas good conductors of
electricity is called metal. Semiconductors are those substance whose conductivity lies
between these two extremes.
Substance for which forbidden energy region is small enough i.e E𝐺 ⋍ 1 𝑒 𝑉, the externally
applied field may carry the particle from valence band to conduction band. These free or
conduction electrons participate in conductivity & substance now become slightly conducting;
it is a semiconductor. The most widely used semiconductor materials are germanium &
silicon having band gaps 0.785 and 1.21 eV respectively. Si atom has 14 protons and 14
electrons. 4valence electrons in outer most orbit indicates Si to be an semiconductor. These Si
atoms combine to form a crystal.
Each Si atom shares its 4 valence electrons
with the 4 neighbouring atoms in order to have
8 valence electrons in its valence orbit.
CLASSIFICATION OF SEMICONDUCTORS:
Conductivity of semiconductors lies in between 105 to 10-4 Siemens per meter. Since
semiconductors have negative coefficient of resistance; their resistance decreases with
increases in temperature. Other important property is that conductivity changes considerably
with addition of even small amount of substances called impurities are added to them.
Semiconductors are classified in following two ways – (a) Intrinsic semiconductor (b)
However, at room temperature some of the covalent bonds are broken due to the thermal
energy of the crystal causing atoms to vibrate. As a result, conduction is possible due to the
availability of charge carriers. The energy EG required to dislodge a valence electron of a
covalent bond & to make it free to participate in conduction is about 0.72eV for
germanium & 1.1eV for Silicon at room temperature. The absence of electron in covalent
bond is represented by a small circle & known as hole. Hole serves as a positive charge
carrier of electricity as effective as a free electron (negative charge).
FLOW OF HOLES:
Free electrons & holes move in opposite direction i.e. free electrons move towards left
along path D,C,B,A. and hole towards right along A,B,C,D,E,F,G acting the same as
Intrinsic semiconductor have small conductivity at room temperature. In order to increase
the conductivity of intrinsic semiconductor a trivalent or pentavalent impurity is added to
the semiconductor. This process of adding trivalent or pentavalent impurity to the pure
semiconductor in order to increase the conductivity is called doping. Doping is done at the
rate such that only one atom of impurity is added per 106 to 1010 semiconductor atoms.
Charge carriers i.e. free electrons or holes can be increased, depending on the type of
impurity (pentavalent or trivalent) added.
Q1. Explain with energy band diagram the difference between insulator, semiconductor and
Q2. Discuss and explain with diagram the difference between intrinsic and extrinsic
Q3. Draw and explain the energy band diagram for n type and p type semiconductors.