Electronic Materials $(20\%)$

$($a$)$ Explain how the band structure of solids gives rise to the electrical properties of metals, semiconductors, and insulators. What is the magnitude of their electrical conductivity and band gap. $(10\%)$

$($b$)$ Explain how temperature changes electrical conductivity for metals and semiconductors. $(5\%)$

$($c$)$ Explain the purpose of doping in semiconductors and how doping affects electrical properties $(5\%)$