Energy Bands in Solids

ENERGY BANDS IN SOLIDS

A solid contains an enormous number of atoms packed closely together. In the case of a single isolated atom, there are discrete energy levels, 1s, 2s, 2p, 3s .... These energy levels can be occupied by the electrons of the atom, as shown in fig. 2.14(a).

All the atoms of a solid, if assumed isolated from one another, can have completely identical electronic schemes of their energy levels. Then the electrons fill the levels in each atom independently.

When the atoms come close together, they strongly interact and the outer electron orbitals overlap with each other.

Hence, the interactions of large number of atoms form closely spaced energy levels known as permitted energy band. The permitted energy bands are separated by energy gap E_g The lower completely filled band is valence band and upper unfilled band is called conduction band (Fig. 2.14(b)).

Definition

A set of such closely spaced energy levels is called an energy band.

Concept of valence band, conduction band and forbidden band

• The energy bands in a solid correspond to the energy levels no in an atom. An electron in a solid can have only those discrete energies that lie within these energy bands. These bands are, therefore, called allowed energy bands.

 • These (allowed) energy bands are, in general, separated by some gaps which have no allowed energy levels. These gap (regions) are known as forbidden energy bands.

• Band corresponding to valence electrons is called valence band and the band beyond forbidden band is called conduction band, into which, the electrons pass, and move freely.

• The electrons in the outermost shell are called valence electrons. The band formed by a series of energy level containing the valence electrons is known as Valence Band.

• Valence band is also defined as a band which is occupied by the valence electrons. The valence band may be partially or completely filled up depending on the nature of the material.

• The next higher permitted band is the conduction band. The energy levels occupying this band is defined as the lowest unfilled energy band. This band may be empty or partially filled. In conduction band, the electrons can move freely.

• Both conduction band and valence bands are separated by a region or gap known as forbidden band or gap which is shown in the fig. 2.15. This band is collectively formed by a series of energy levels above top of the valence band and below the bottom of the conduction band.

• The energy gap between the valence band and conduction band is called the forbidden energy gap or forbidden band

It should be noted that no electron can exist in this band. When an electron in the valence band absorbs enough energy, it crosses the forbidden gap and enters into the conduction band. (Fig. 2.16)

Classification of Metals, Semiconductors and Insulators

On the basis of width of forbidden gap valence and conduction band the solids are classified into insulators, semiconductors and conductors.

Insulators

• The band structure of insulators is as shown in fig. 2.17.

• The energy gap between conduction band and valence band is very high and is about 10 eV.

• The forbidden energy band is very wide. Due to this, electrons cannot jump from valence band to conduction band. In insulator, the valence electrons are bound very bas tightly to their parent atoms.

• The conduction band is completely vacant and valence band is completely filled.

• Even at high electric field, no electron will jump from valence band to the conduction band because of large energy gap. Hence, the electrical conductivity is zero.

Semiconductors

• The band structure of semiconductors is as shown in fig. 2.18.

• The forbidden gap is very small. Germanium and Silicon are the best examples of semiconductors.

• The energy gap between conduction band and valence band is very small. It is about 0.5 eV to 1 eV.

• As temperature increases, the bonds in the valence band break up and the created electrons move from valence band to the conduction. The vacancies created in the valence ba band due to breaking of bonds are termed as holes.

• Hence, conduction band is partially filled and valence dale band is partially vacant. These electrons and holes are responsible for electrical conduction.

Conductor

The band structure of conductors is as shown in fig. 2.19.

 There is no forbidden gap, both valence and conduction bands overlap each other.

• The electrons free to move within the conductor are responsible for electrical conduction.

•  As temperature increases, the electrical conduction decreases, because mobility decreases due to large number of collisions with ions.

• The most important fact in conductors is that due to the absence of forbidden gap, there is no structure to establish holes. The total current in conductors is due to only the flow of electrons.