First-Principles Study of Dielectric Properties of Amorphous High-$k$ Materials

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The dielectric properties of amorphous alumina ($a$-Al2O3), hafnia ($a$-HfO2), and hafnium aluminate ($a$-HfAlO) having a $\text{Hf}/(\text{Al}+\text{Hf})$ ratio of 20% have been studied by the first-principles calculation. The calculated dielectric constants of amorphous model structures increase with increasing $\text{Hf}/(\text{Al}+\text{Hf})$ ratio in terms of both electronic and lattice polarization contributions. The lattice polarization contribution to the dielectric constants is larger than the electronic one. The calculated dielectric functions of the amorphous models show a negligible frequency dispersion at the operation frequencies of current complementary metal–oxide–semiconductor (CMOS) transistors. However, the dielectric functions of the amorphous models have high peaks at much lower frequencies from about 1 THz than those of $\alpha$-alumina ($\alpha$-Al2O3) and monoclinic hafnia ($m$-HfO2) crystals.
2007-05-30