$4)$ Provide your analysis on how material's properties influence the characteristics and performance of a MOSFET. For that, compare monocrystalline silicon, gallium arsenide, and zinc oxide as model semiconductors. Consider factors such as band gap, electron mobility, and thermal conductivity. What would be the difference in these materials' usage in MOSFET?

Guiding questions:

$-$ How do the intrinsic properties of these materials affect the on$-$state current and off$-$state leakage current of the MOSFET?

$-$ What trade$-$offs exist when choosing one material over another in terms of power efficiency and speed?

$-$ How does device scaling $($e$.$g$.,$ moving to smaller size of a single MOSFET$)$ affect these materials differently?