4. (a) Explain the concept of (i) intrinsic, (ii) n-type, and (iii) p-type semiconductors with the aid of bond diagrams and band diagrams.

(b) What is a hole? Using a mathematical derivation to show that the holes behave like positive charges.

(c) Explain with the aid of Fermi-Dirac distribution function that at 0° K, all the energy states in the valence band of silicon are filled and all the energy states in the conduction band are empty.

(d) Why it is necessary to use effective mass instead of real mass for electrons in the analysis of semiconductor materials and mention why different effective masses are to be used for different types of semiconductors,

(e) Explain (a) bonding orbital and (b) anti-bonding orbital.