Anomalous Behavior of the Dielectric Constant of Hafnium Silicates: A First Principles Study

We present an extensive ab initio study of the structural and dielectric properties of hafnium silicates ${\mathrm{Hf}}_x{\mathrm{Si}}_{1-x}{\mathrm{O}}_2$ that accounts for the observed anomalous dependence on composition of the static dielectric constant in the entire $x$ range. The results reveal that this complex behavior reflects that of the structural development with $x$, from silica to hafnia, and clarify how different growth processes can also lead to scattered sets of data. Several simple models proposed thus far to explain part of the experimental data are shown to be inadequate. It is argued that silicate layers with low hafnium content form at the ${\mathrm{HfO}}_2/\mathrm{Si}$ interface and play a crucial role in preserving high electron mobility in the channel.

Figure 1

Dielectric constant vs Hf concentration. (a) Experimental data from Refs. 7 (blue), 18 (turquoise), 21 (green), 8 (magenta), [3b] (orange), 19 (red), 10b (black), 32 (brown), and 20 (violet). (b) Our ab initio calculations for the thermodynamically favored (blue) and some disfavored structures (red), and “amorphous” silica samples (green triangles) (see text). $*$ stands for configurations with uniform distribution, ● for nonuniform.

Figure 2

Radial distribution functions (a) and current CN (b) for $x=0.25$ (solid) and $x=0.75$ (dashed). Black lines refer to $\alpha$-cristobalite (solid) and $t\mathrm{\text{−}}{\mathrm{HfO}}_2$ (dashed); bond-angle distribution (c) for $x=0.25$.

Figure 3

Dielectric constant: (a) Comparison of our ab initio calculations ${ϵ}_0$ and the CN-dependent model of Ref. 25. (b) Missing correlation with the average molecular volume.