Question

1. Why is the conductivity of metal different from the insulator? - How different is the semiconductor from them?

2. What is the main cause of the energy gap? How is it related to the Bragg condition.

3. How is Bloch function different from the general wavefunction?

Answer 1

Ans:1;

Insulator: materials through which electricity cannot pass are called insulators. Plastic, glass, wood etc are the examples of insulators. The valence band of those material remains full of electrons. The conduction band of those material remains empty. The forbidden energy gap between the conduction band and the valence band is widest. The difference is more than 10ev. Crossing the forbidden energy gap from valence band to conduction band requires large amount of energy.

Conductors:  
valence band and the conduction band of conductors overlap each other. There is no forbidden energy gap here so Eg=0. At absolute zero temperature large number of electrons remain in the conduction band. The resistance of conductor is very low, a large number charge carriers are available here. So, the electricity can pass easily through the conductors.

Now, semiconductors

Semiconductors are those materials whose electrical conductivity is between conductors and insulators. The forbidden energy gap of a semiconductor is nearly same as insulator. The energy gap is narrower. The value of Eg =1.1eV for silicon crystal and Eg =0.7eV for germanium at ok. It can easily overcome due to thermal agitation or light. A semiconductor has partially full valence band and partially full conduction band at the room temperature. The conduction band remains fully empty and the valence band remains full of electrons at absolute zero temperature. So, silicon and germanium are insulators at absolute zero temperature. On the other hand with the increasing of temperature the electrical conductivity of semiconductors increase.

Ans:2; The energy bands in solids appear because a) the potential energy for electrons in a crystal is periodic in space and b) because electrons obey quantum mechanics (in some sense they behave like waves).

Ans:3; A Bloch wavefunction is a type of wavefunction for a particle in a periodically-repeating environment, most commonly an electron in a crystal. A wavefunction ψ is a Bloch wave if it has the form

where r is position, ψ is the Bloch wave, u is a periodic function with the same periodicity as the crystal, k is a vector of real numbers called the crystal wave vector, e is Euler's number, and i is the imaginary unit. In other words, if we multiply a plane wave by a periodic function, we get a Bloch wave.