Origin of the Flatband-Voltage Roll-Off Phenomenon in Metal/High- $k$ Gate Stacks

Abstract

The effect of flatband-voltage reduction [roll-off (R-O)], which limits fabrication options for obtaining the needed band-edge threshold voltage values in transistors with highly scaled metal/high- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$k$</tex></formula> dielectric gate stacks, is discussed. The proposed mechanism causing this R-O phenomenon is suggested to be associated with the generation of positively charged oxygen vacancies in the interfacial <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\hbox{SiO}_{2}$</tex></formula> layer next to the Si substrate. The vacancies in the interfacial layer are induced by oxygen outdiffusing into the overlying high- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX"> $k$</tex></formula> dielectric. The model is consistent with the variety of observations of R-O dependence on the electrode and substrate type, high- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$k$</tex></formula> dielectric composition and thickness, temperature, etc. The model's predictions were experimentally verified.