Describe the energy band structure available to electrons moving in crystalline materials. How can it be used to explain the properties of crystalline materials that are conductors, insulators and semiconductors?

Where does the Fermi energy lie in an intrinsic semiconductor? Describe the process of doping of semiconductors and explain the difference between $n$-type and $p$-type doping. What is the effect of the doping on the position of the Fermi energy in the two cases?

Why is there a potential difference across a junction of $n$-type and $p$-type semiconductors?

Derive the relation

$$I=I_{0}\left(1-e^{-q V / k T}\right)$$

between the current, $I$, and the voltage, $V$, across an $n p$ junction, where $I_{0}$ is the total minority current in the semiconductor and $q$ is the charge on the electron, $T$ is the temperature and $k$ is Boltzmann's constant. Your derivation should include an explanation of the terms majority current and minority current.

Why can the $n p$ junction act as a rectifier?