Theoretical calculations for high-k dielectrics

The purpose of these calculations is to assist development of gate dielectrics for new generations of MOS transistors. The primary practical issue is to achieve the Equivalent Oxide Thickness (EOT) as low as 1 nm and less. EOT is associated with general features of the film morphology. In particular, the chemical composition of the film is a function of the distance from the substrate, affecting the effective dielectric constant of the film. Moreover, the density of charge traps (fixed and reloadable) in the film and at the interface must be brought down to a value comparable to that typical for industrial quality gate SiO₂. Our theoretical work has so far been focused on the analysis of atomistic aspects of these issues for the family of high-k dielectrics containing praseodymium oxides: PrO_x, Pr silicate, Pr aluminate, Pr titanate. In 2007, we have started calculations for other materials, as strontium tantalate. Our atomistic calculations are done within DFT framework.

Within the frame of this project, we have so far understood several essential properties of Pr oxides, silicates and silicides, starting from band structure calculations (which we conducted also for a range of other metal oxides and chalcogenides). In particular, we gained insight into the fundamental interfacial structures and interface layer formation mechanisms associated with Pr oxide and silicate growth on Si(001) and Si(111), including the film surface roughness, the substrate oxidation and intermixing, estimate of the misfit dangling bond density at the Pr₂O₃/Si(100) interface, the mechanism governing the stacking order of hexagonal Pr₂O₃ and Y₂O₃ on Si(111), energies and electrical behaviour of some native defects and critical impurities, and the evolution of the interfacial dipole during oxidation. We addressed the chemical reactions pertinent to silicate film growth by solid state reaction between SiO₂ and a Pr-containing layer, including the energetics of Pr impurities in amorphous SiO₂ and oxidation of Pr₂Si₂O₇. We analysed the process of the interface state passivation by remote action of Ti, and the onset of interface silicide growth. We systematically investigated the native defects in bulk Pr₂O₃, PrO₂, Pr₂Si₂O₇, PrAlO₃, and (to only certain extent) in Pr₂Ti₂O₇ and SrTa₂O₆. We considered the segregation of atoms from the substrate and/or metal gate (Si, B, Ti, N) into the dielectric film and of metal atoms (Pr, Ti) into Si substrate and into SiO₂ interface layer, the dissolution of H₂O, and the influence of moisture on the intermixing with Si from the substrate. We formulated a consistent model of positive fixed charge formation which we argue to be valid in high-k oxides as well as in SiO₂. We investigated the electrical conductivity mechanism in PrO_x. Finally, we also studied the effect of carbon and nitrogen contamination of HfO₂, focusing on substitutional and interstitial CN.

We begin with a few words on the theoretical method (Section Approach) and on praseodymium oxides in general (Section Bulk Pr Oxides). After that, we describe in more detail some of the results mentioned above (Section Selected Results).

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