A pure (99.9%) Si & Ge crystal is known as intrinsic semiconductors. In a Si crystal, every Si atom shares its four valence electrons with 4 neighboring atoms and thereby forms 4 covalent bonds. So at low temperature, every valence electrons present in the crystal is in the bond. In the equivalent band theory, these electrons are said to be present in the valence band.
When such a crystal is brought to the room temperature, some of the electrons originally present in the bond get enough energy [more than bond energy], so that they can break the band and become free. These electrons leave behind a positively charged region in the bond, which is called ‘hole’ and acts as an electrons trap. The hole behaves as an apparent free particle with effective positive charge. Thus in intrinsic semiconductors free electrons & holes are generated in pair.
This phenomenon is shown as a transition of electron from Valence Band to the Conduction Band, in energy band diagram and it is called intrinsic transition. So, intrinsic transition generates a ‘free electron’ in Conduction Band and a ‘hole’ in Valence Band.
So, at any instant and at any temperature.
The number of holes per unit volume (nh)i is equal to number of free electrons (ne)i
i.e. (ne)i = (nh)I = ni
where ni is called intrinsic carrier concentration.
Whenever a potential difference is applied across the ends of a semiconductor, an electric field is generated inside it. Due to this electric field, every electron experience an electrostatic force in the direction opposite to the electric field and the free electrons move with drift velocity in the direction opposite to the field and thereby generates current Ie ,in the direction of field. The holes also effectively move in the direction of the field, jumping from one bond to another bond. Due to this movement of holes, a hole current (Ih) is generated, in the direction of the field. So, in semiconductors both free electrons as well as holes act as charge carriers.
Also the total current flowing through the semiconductor is the sum of the current generated by the electrons and by the holes.
I = I e + I h
It may be noted that, apart from the process of generation of conduction electrons and holes, a simultaneous process of recombination of the electrons with the holes occurs. At equilibrium, the rate of generation (of electron and hole pair) is equal to the rate of recombination of charge carriers. The recombination occurs due to an electron colliding with a hole.
