Square roots of elliptic second order divergence operators on strongly lipschitz domains:<Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript> theory

We prove the Kato conjecture for square roots of elliptic second order non-self-adjoint operators in divergence formL = -div(A∇) on strongly Lipschitz domains in ℝⁿ, n≥2, subject to Dirichlet or to Neumann boundary conditions. The method relies on a transference procedure from the recent positive result on ℝⁿ in [2].     

Experimental results and basic considerations concerning injection and transport of electrons in the dye-sensitized colloidal sponge-type anatase TiO2 electrode

Electron transfer over the reaction distance corresponding to three saturated bonds occurs within 70 fs from the excited singlet state of anchored perylene chromophores to empty electronic levels in a sponge-type anatase TiO₂ electrode. Injected electrons can be consumed in three different types of recombination processes at the interface with the electrolytic contact. Electron transport through the electrode follows a potential gradient that is set-up in the dark, corresponding to the difference between the Fermi levels of the two contact materials. It is dominated by multiple trapping and trap filling processes.     

Complex interface and growth analysis of single crystalline epi‐Si(111)/Y2O3/ Pr2O3/Si(111) heterostructures: Strain engineering by oxide buffer control

Complex oxide heterostructures on Si gain in the field of engineered Si wafers increasing interest as flexible buffer systems for developing virtual Si substrates. Strain engineering of thin epitaxial Si thin films on insulating oxide buffers is of special interest to boost charge carrier mobility for Silicon‐on‐Insulator (SOI) technologies. The single crystalline Si(111)/Y₂O₃ (111)/Pr₂O₃ (111)/Si(111) heterostructure offers, in principle, the opportunity to grow strain‐engineered epitaxial Si(111) layers, realizing compressed, fully relaxed, as well as tensile‐strained Si films. This flexibility is based on a thickness‐dependence of the Y₂O₃ lattice constant in the oxide bi‐layer buffer: In theory, the Y₂O₃ buffer lattice constant on Pr₂O₃/Si(111) can change from pseudomorphism (bigger than Si) over the Si lattice constant towards a fully relaxed status (smaller than Si). By a detailed interface analysis, using TEM‐EELS in combination with an in‐situ RHEED–XPS study of the isomorphic Y₂O₃ growth on Pr₂O₃/Si(111), the physical origin of this Y₂O₃ buffer lattice constant variation is identified. It is possible to discriminate between the contributions from chemical mixing effects between the isomorphic oxides Y₂O₃ and Pr₂O₃ on the one hand and true misfit strain relaxation mechanisms in stoichiometric Y₂O₃ on the other hand. Copyright © 2010 John Wiley & Sons, Ltd.