(La₂O₃)_1-x (Al₂O₃) _x composite films (La₂O₃:Al₂O₃ = 100:0, 80:20, 67:33, 50:50) were synthesized using pulsed laser deposition. We investigated their thermal stability and electrical properties as high dielectric constant gate dielectric films. La₂O₃ (an Al₂O₃ content of 0%) films were uniformly crystallized as La-silicate after rapid thermal annealing (RTA) at 1000°C for 15 s in an N₂ ambient. We found that the addition of Al₂O₃ suppresses crystallization, and amorphous structures are retained in the samples with an Al₂O₃ content of 33% or greater. Furthermore, Al₂O₃ addition suppresses diffusion of Si into upper composite films during RTA. The smallest capacitance equivalent oxide thickness of 1.2 nm was achieved for a sample with an Al₂O₃ content of 20% and with leakage current density of 3.9×10^-3 A/cm² at + 1 V relative to the flat band voltage.

We introduce the concept of a handlebody decomposition of a 3-manifold, a generalization of a Heegaard splitting, or a trisection. We show that two handlebody decompositions of a closed orientable 3-manifold are stably equivalent. As an application to materials science, we consider a mathematical model of polycontinuous patterns and discuss a topological study of microphase separation of a block copolymer melt.

In this paper, we consider decompositions of closed orientable 3-manifolds with more than 3 handlebodies, where the union of intersections of handlebodies is a multibranched surface. We define stabilization operations for such decompositions and show the stable equivalence.