Question $4(20$ marks$)$

$($a$)$ Explain how the drift current in semiconductors is generated.

$($b$)$ Explain which drift current component is dominant in:

$($i$)$ n$-$type semiconductors.

$($ii$)$ p$-$type semiconductors.

$($c$)$ Given that at temperature of $300$ K $,$ an electric field applied to an extrinsic gallium arsenide sample causes equal electron and hole current densities. Determine:

$($i$)$ the ratio of the equilibrium hole density to the equilibrium electron density.

$($ii$)$ the equilibrium electron and hole densities.

$($iii$)$ the net doping concentration.