Electrical characteristics of metala€“insulatora€“semiconductor and metala€“insulatora€“semiconductora€“insulatora€“metal capacitors under different high-$k$ gate dielectrics investigated in the semi-classical and quantum mechanical models

摘要

In this paper the electrical characteristics of metala€“insulatora€“semiconductor (MIS) and metala€“insulatora€“semiconductora€“insulatora€“metal (MISIM) capacitors with (100)-oriented p-type silicon as a substrate under different high-$k$ gate dielectrics (SiO$_2$, HfO$_2$, La$_2$O$_3$ and TiO$_2$) are investigated in the semi-classical and quantum mechanical models. We review the quantum correction in the inversion layer charge density for p-doped structures. The purpose of this paper is to point out the differences between the semi-classical and quantum mechanical charge descriptions at the insulatora€“semiconductor interface and the effect of the type of oxide and their position (gate oxide or buried oxide) in our structures. In particular, capacitancea€“voltage ($Ca€“V$), relative position of the sub-band energies and their wavefunctions are studied to examine qualitatively and quantitatively the electron states and charging mechanisms in our devices. We find that parameters such as threshold voltage and device trans-conductance are enormously sensitive to the proper treatment of quantization effects.