Classification of Metals, Conductors , Insulator and semiconductors on the basis of their conductivity and Energy Bands :
Classification of Metals, Conductors , Insulator and semiconductors on the basis of their conductivity
Different solids are classified into three categories namely metals (or conductors), insulators and semiconductors on the basis of the values of their resistivity or conductivity.
(i) Metallic conductor :
The substances having very low value of resistivity or very high value of conductivity are termed as metals. The order of the resistivity of metals is $10^{-2}$ to $10^{-8} \Omega$ m. Since, conductivity ($\sigma$) is inversely proportional to the resistivity ($\rho$), i.e., $\sigma = 1/\rho$, therefore, the order of conductivity of the metals is $10^{2}$ to $10^{8} \text{S m}^{-1}$.
For example: silver, copper, aluminium, tungsten, mercury etc.
(ii) Insulators
The solids having very high value of resistivity or very low value of conductivity are termed as insulators. The order of the resistivity ($\rho$) of the insulators is $10^{11}$ to $10^{19} \Omega$ m. However, the order of conductivity ($\sigma$) of the insulators is $10^{-11}$ to $10^{-19} \text{S m}^{-1}$.
For example: wood, glass, quartz, diamond, ebonite, paper etc
(iii) Semiconductors
The solids having resistivity or conductivity in between metals and insulators are termed as semiconductors. The order of the resistivity of semiconductors is $10^{-5}$ to $10^{6} \Omega$ m. However, the order of conductivity of the semiconductors is $10^{5}$ to $10^{-6}$
Classification of Metals, Conductors , Insulator and semiconductors on the basis of Energy Bands :
Solids can be classified into different categories on the basis of energy bands. We can distinguish among metals (or conductors), insulators and semiconductors on the basis of energy bands.
(i) Metals or conductors :
A solid in which valence band and conduction band are partially filled or valence band and conduction band overlap is known as metal or conductor. In the case shown in figure 1 the conduction band and valence band are partially filled.
In the case shown in figure 2, there is no forbidden energy gap between the valence band and the conduction band.
In case of partially filled valence band, electrons from filled energy levels can move easily to the unfilled higher energy levels and hence conduction of electrons takes place. In case of the overlap of valence and conduction bands, electrons move easily from valence band to the conduction band. Thus, large number of electrons are available for the conduction of electricity (or electric charge). Hence, metals or conductors are good conductors of electricity.
(ii) Insulators :
In insulators, the valence band is completely filled with electrons and the conduction band is empty and both the bands are separated by a forbidden energy gap of about greater than $3 \, \text{eV}$.
There is no electron in the conduction band and hence insulator cannot conduct electric current. The insulator can conduct electric current only if the electrons from the valence band can move to the conduction band. This can happen if the energy gained by electrons in the valence band is greater than $E_g$. But the electrons in the valence band have energy $\approx \frac{3}{2} kT = 0.025 \, \text{eV}$ (where $k$ is the Boltzmann's constant) at room temperature. This energy is very small as compared to the energy of the forbidden energy gap. Therefore, the electrons in the valence band cannot go to the conduction band and hence insulator cannot conduct electric current. Therefore, insulator is a bad conductor of electricity.
(iii) Semiconductors :
Semiconductors are the materials in which the forbidden energy gap between the filled valence band and the empty conduction band is very small (i.e., $\sim 1 \, \text{eV}$).
Germanium and silicon are the examples of semiconductors. In case of silicon, the forbidden energy gap ($E_g$) at room temperature is about $1.2 \, \text{eV}$ and for Germanium it is about $0.72 \, \text{eV}$.
At $0 \, \text{K}$, the electrons in the valence band do not have sufficient energy to jump to the conduction band and hence semiconductor behaves as an insulator at $0 \, \text{K}$. But at room temperature, some of the electrons in the valence band have sufficient thermal energy to jump to the conduction band and a semiconductor can conduct even at room temperature. Thus, semiconductor behaves as an insulator at $0 \, \text{K}$ but semiconductor behaves as a conductor at room temperature.