CLASSIFICATION OF CONDUCTORS, SEMICONDUCTORS AND INSULATORS -

On the basis of conductivity( $\dpi{120} \fn_cm \sigma$ ) or resistivity( $\dpi{120} \fn_cm \rho$ )

On the basis of conductivity( $\dpi{120} \fn_cm \sigma$ ) or resistivity( $\dpi{120} \fn_cm \rho =\frac{1}{\sigma }$ ), the solids are classified as Metals, Insulators and Semiconductors

1. Metals:- They possess very low resistivity ( or high conductivity)

$\dpi{120} \fn_cm \rho \sim 10^{-2} - 10^{-8} \;\Omega\;m$

$\dpi{120} \fn_cm \sigma \sim 10^{2} - 10^{8} \;S\;m^{-1}$

2. Semiconductors:- They have resistivity or conductivity intermediate to metals and insulators.

$\dpi{120} \fn_cm \rho \sim 10^{-5} - 10^{6} \;\Omega\;m$

$\dpi{120} \fn_cm \sigma \sim 10^{5} - 10^{-6} \;S\;m^{-1}$

3. Insulators:- They have high resistivity ( or low conductivity)

$\dpi{120} \fn_cm \rho \sim 10^{11} - 10^{19} \;\Omega\;m$

$\dpi{120} \fn_cm \sigma \sim 10^{-11} - 10^{-19} \;S\;m^{-1}$

It is important to note that these values are indicative and could go outside the range as well.

Types of semiconductors on the basis of availability:-

1. Elemental Semiconductors:- available naturally like Pure Silicon (Si) and Pure Germanium (Ge)

2. Compound Semiconductors:- made by compounding two or more metals together. They are sub-divided into these categories:

a. Inorganic – like Cadmium Sulphate(CdS), Gallium Arsenide (GaAs), Cadmium Selenide (CdSe), Indium Phosphate (InP) etc.

b. Organic – like anthracene, doped phthalocyanine, etc.

c. Organic polymers – like polypyrrole, polyaniline, polythiophene, etc.

most of the currently available semiconductor devices make use of elemental semiconductors Si or Ge and Inorganic Compound. After 1990, semiconductor devices using organic semiconductors and semiconducting polymers have been developed.

On the basis of energy band

In an isolated atom the energy of any of its electrons is decided by the orbit in which it revolves. But in the case of solid the atoms are arranged in a systematic space lattice and influenced by neighbouring atoms. Inside the crystal, each electron has a unique position and no two electrons see exactly the same pattern of surrounding charges. Because of this, each electron will have a different energy level. This would make the nature of electron motion in a solid very different from that in an isolated atom.

These different energy levels with continuous energy variation form what are called energy bands. The bands of energy levels are referred to the entire solid as a whole and not a single individual atom.

Valance band (V.B), Conduction band(C. B) and Forbidden energy gap (F. E. G)

We know that electrons in the outermost shell are called valance electrons and the band which is occupied by the valance electrons is called the valance band. The valance band may be partially or completely filled. This band can never empty.

In certain materials (metals) the valance electrons are loosely attached to the nucleus. Even at ordinary temperature some of the valence electrons left the valence band. These are called free electrons. The band occupied by these electrons is called the conduction band. This band may be empty or partially filled. generally, insulators have an empty conduction band.

Let us consider the case of Si or Ge crystal containing N atoms. The number of electrons in the outermost orbit is 4 ( 2s and 2p electrons). The maximum possible number of electrons in the outer orbit is 8 (2s and 6p electrons). So, for the 4N valance electrons, there are 8N available energy states. These 8N discrete energy levels can either form a continuous band or they may be grouped in different bands depending upon the distance between the atoms in the crystal.

In the case of Si or Ge, these 8N states are split apart into two bands which are separated by an energy gap ( $\dpi{120} \fn_cm E_g$ )

From fig $\dpi{120} \fn_cm E_c$ is the lowest energy level in the conduction band and $\dpi{120} \fn_cm E_v$ is the highest energy level in the valance band. Above $\dpi{120} \fn_cm E_c$ and below $\dpi{120} \fn_cm E_v$ , there are a large number of closely spaced energy levels. The gap between the top of the V.B and the bottom of the C.B is called Forbidden energy gap (F.E.G) / Energy band gap ( $\dpi{120} \fn_cm E_g$ )

Insulators, Semiconductors and Conductors

Insulator:- In the case of insulators, the F.E.G is very wide ( $\dpi{120} \fn_cm E_g>3eV$ ). Due to this fact electrons cannot jump from V.B to C.B. In insulators the valance electrons are bound very tightly to their parent atoms. when very high energy is supplied, electrons may be able to jump across the F.E.G.

Semiconductors:- In semiconductors, the F. E. G is very small. In Ge, the energy gap is of the order of 0.7 eV while in the case of Si, it is of the order of 1.1 eV. At $\dpi{120} \fn_cm 0^0$ K, there are no electrons in C.B. However with the increase in temperature ( at room temperature) some electrons are liberated into the C.B. In other words conductivity of semiconductors increases with temperature.

Conductors:- In the case of conductors, there is no forbidden energy gap and the V.B and C.B overlap each other. The electrons from V.B freely enter into C.B. “The most important point in conductors is that due to the absence of F.E.G, there is no structure to establish holes.”

Hole formation and its movement in semiconductors:-

At room temperature, some of the covalent bonds are broken due to the thermal energy supplied to the crystal. Due to the breaking of the bonds, some electrons become free and move to C.B. The absence of electrons in the covalent bond ( inside V.B) is represented by a small circle.

This empty place or vacancy left behind in the crystal structure is called a hole. Since an electron has a unit -ve charge, the hole carries a unit +ve charge.

When an electric field is set up inside a semiconductor, an electron at B from an adjacent atom jumps into the hole at A. This fills the original hole but creates a new hole at B. Next, an electron at C jumps into the hole at B and so on. i.e -ve charge (valance electron) is moved from E to A. But it is more convenient to consider as if +ve hole has moved from A to E.

NOTE:-

Here electrons move from an adjacent atom without passing through the F.E.G. i.e holes movement takes place in V.B only.
Semiconductors possess unique properties in which apart from electrons the holes also moves.
Electronic current is in the conduction band but hole current is in the valance band.
Conduction electrons move almost twice as fast as the holes.

On the basis of conductivity() or resistivity()