In high$-$k MOS structures, both thermionic emission and Frenkel$-$Poole emission are significant leakage

mechanisms. Research and discuss: $(1)$ how the dominance of these mechanisms changes with different

operating temperatures and electric field strengths, $(2)$ how these leakage mechanisms affect the

performance of advanced process node $(5$nm and below$)$ logic devices, and $(3)$ propose possible

engineering solutions to suppress these leakage currents.