  High-$\kappa$ metal oxides are a class of materials playing an increasingly
important role in modern device physics and technology. Here we report
theoretical investigations of the properties of structural and lattice
dielectric constants of bulk amorphous metal oxides by a combined approach of
classical molecular dynamics (MD) - for structure evolution, and quantum
mechanical first principles density function theory (DFT) - for electronic
structure analysis. Using classical MD based on the Born-Mayer-Buckingham
potential function within a melt and quench scheme, amorphous structures of
high-$\kappa$ metal oxides Hf$_{1-x}$Zr$_x$O$_2$ with different values of the
concentration $x$, are generated. The coordination numbers and the radial
distribution functions of the structures are in good agreement with the
corresponding experimental data. We then calculate the lattice dielectric
constants of the materials from quantum mechanical first principles, and the
values averaged over an ensemble of samples agree well with the available
experimental data, and are very close to the dielectric constants of their
cubic form.
