Realisation and metrological characterisation of thickness standards below 100 nm

High-accuracy film thickness measurements in the range below 100 nm can be made by various complex methods like spectral ellipsometry (SE), scanning force microscopy (SFM), grazing incidence X-ray reflectometry (GIXR), or X-ray fluorescence analysis (XRF). The measurement results achieved with these methods are based on different interactions between the film and the probe. A key question in nanotechnology is how to achieve consistent results on a level of uncertainty below one nanometre with different techniques.Two different types of thickness standards are realised. Metal film standards for X-ray techniques in the thickness range 10 to 50 nm are calibrated by GIXR with monochromatised synchrotron radiation of 8048 eV. The results obtained at four different facilities show excellent agreement. SiO₂ on Si standards for SE and SFM in the thickness range 6 to 1000 nm are calibrated by GIXR with monochromatised synchrotron radiation of 1841 eV and with a metrological SFM. Consistent results within the combined uncertainties are obtained with the two methods. Surfaces and interfaces of both types of standards are additionally investigated by transmission electron microscopy (TEM). PACS 61.10.Kw; 68.55.Jk; 06.20.Fn; 06.60.Mr; 07.79.Lh     

Characterization of organic thin films with resonant soft X-ray scattering and reflectivity near the carbon and fluorine absorption edges

The use of soft X-rays near the carbon absorption edge (∼270–300 eV) for small angle X-ray scattering and X-ray reflectivity experiments has significantly expanded the scientific capabilities to investigate thin films of soft matter that are primarily composed of carbon and low Z heteroatoms. In this perspective, we will delineate the basic operating principles and underlying physics of these methods and exemplify their impact by discussing a few recent applications. An extension of these methods to the fluorine edge is also included, demonstrating that the general concepts are also applicable to absorption edges of hetero atoms in soft matter. A short perspective of some future developments is provided.     

Existenzsätze für schwach nichtlineare Operatorgleichungen und Anwendung auf Randwertaufgaben mit gewöhnlichen Differentialgleichungen

With Schauder's fixpoint principle we establish an existence theorem for solutions of two simultaneous nonlinear operator equations of the formL _iu=M_iu, i=1,2, L_i linear,M _i continous. By applying this result to boundary value problems with ordinary differential equations we generalize results of Conti and Ehrmann in various directions.     

Substrate effect on the melting temperature of thin polyethylene films

Strong dependence of the crystal orientation, morphology, and melting temperature (Tm) on the substrate is observed in the semicrystalline polyethylene thin films. The Tm decreases with the film thickness decrease when the film is thinner than a certain critical thickness, and the magnitude of the depression increases with increasing surface interaction. We attribute the large Tm depression to the decrease in the overall free energy on melting, which is caused by the substrate attraction force to the chains that competes against the interchain force which drives the chains to crystallization.     

Synthesis,Single Crystal Growth and Crystal Structure of Ta7Cu10Ga34 – a 8 × 4 × 2 Super Structure of CsCl

Single crystals of Ta₇Cu₁₀Ga₃₄ were grown from the elements in a Cu/Ga melt. Ta₇Cu₁₀Ga₃₄ represents the first ternary compound of the system Ta/Cu/Ga. The crystal structure (Cmmm, oC102, Z = 2, a = 23.803(1), b = 12.2087(4), c = 5.7487(2) Å, 1291 refl. 78 parameters, R₁ = 0.037, wR₂ = 0.070). The crystal structure is characterized by rods of pentagonal prisms MGa₁₀, which are alternatingly occupied by Ta and Cu. Four of these rods are connected to columns running in direction (001). These columns are linked by cubic units TaGa₈, CuGa₈, and GaGa₈. According to the characteristic structural elements and the size of the unit cell Ta₇Cu₁₀Ga₃₄ represents a 8 × 4 × 2 super structure of CsCl or bcc. With respect to the underlying CsCl structure the formula can be written as [Ta₇Cu₁₀Ga₂□₁₃]Ga₃₂, i.e. a cubic primitive packing of 32 Ga atoms with Ta, Cu, and Ga in cubic voids and 13 vacancies. The pentagonal‐prismatic coordination of Ta and Cu can formally be obtained from the cubic primitive packing of Ga atoms by a 45° rotation of a part of the Ga₈ cubes. There is a close similarity to the binary compounds Ta₈Ga₄₁ and Ta_2–xGa_5+x. The first one is also related to a CsCl‐like structure, the latter one contains rods of pentagonal prisms, which form the same columns. There are also relations to the ternaries V₂Cu₃Ga₈ and V₁₁Cu₉Ga₄₆, whose cubic structures are more or less complex variants of CsCl.     

X-ray microscopy of novel thermoplastic/liquid crystalline polymer blends by mechanical alloying

Incorporation of liquid crystalline polymers (LCPs) into commodity polymers remains a challenge in the design of high-performance, low-cost polymeric blends. Blends of a thermoplastic polymer and a nematic LCP are produced here by mechanical alloying. Functionality sensitive X-ray microscopy reveals LCP dispersions as small as 100 nm in diameter. Intimate mixing remains upon subsequent melt processing, indicating that mechanical alloying is suited for applications such as recycling.     

B4 Tetrahedra for Aluminum Atoms—A Surprising Substitution in τ-Borides Ni20Al3B6 and Ni20AlB14

Stabilized by the tailor-made coordination in the crystal , B₄ tetrahedra were characterized for the first time in a solid-state structure (shown on the right). Some of the Al atoms are replaced by B₄ tetrahedra in the cubic τ-boride Ni₂₀AlB₁₄. The B–B distances of 1.681(15) Å are similar to those in the molecular structures of B₄Cl₄ and B₄(tBu)₄, which contain tetrahedral B₄ units.     

Synthese und Kristallstruktur von Ti12Sn3O10 – einem niedervalenten Oxid des Titans mit oxidischem Gerüst und intermetallischen „Inseln”︁

Synthesis and Crystal Structure of Ti₁₂Sn₃O₁₀ – a Low Valent Oxide of Titanium with an Oxidic Network and Intermetallic ”︁Islands”︁”︁ The new ternary compound Ti₁₂Sn₃O₁₀ is obtained by the reaction of Ti, TiO₂ and Sn at 1500 °C. According to the single crystal structure analysis (cubic, space group Fm3m, a = 13.5652(9) Å, Z = 8, wR₂(I) = 0.048, R₁(F) = 0.020) the air stable compound represents a new structure type combining structural features of oxides and intermetallics. While tin is surrounded only by titanium the five different Ti atoms have oxidic and metallic coordination spheres as well, explaining the quite low averaged oxidation number. The crystal structure is characterized by a threedimensional net of Ti₄O‐tetrahedra and trigonal bipyramides Ti₅O. In the voids there are intermetallic ”︁islands”︁”︁ of a composition Ti₃₃Sn₆ with a diameter of about 10 Å.     

Optical study of single InAs on In0.12Ga0.88As self-assembled quantum dots: biexciton binding energy dependence on the dots size

Single self-assembled InAs quantum dots embedded in a In_0.12Ga_0.88As quantum well and emitting in the near infrared have been optically investigated. The dependence on the excitation power of the single quantum dot photoluminescence has been used to identify the emission of the biexciton complex. The biexciton binding energy, which has been measured for a dozen dots, increases with increasing exciton transition energy for the dot sizes investigated in the present work, as a consequence of stronger confinement in a smaller quantum dot. The obtained data is compared with experimental results available in the literature for InAs quantum dots. PACS 78.67.Hc; 73.21.La; 78.55.Cr     

Kinetics and mechanisms of the redox reaction of hexaaquotitanium(III) and the ethylenediamine tetraacetato titanium(III) complex by aqueous solutions of bromine

At 25°C, I = 1.0 M (CF₃SO₃⁻Li⁺+CF₃SO₃H), [H⁺] = 0.034–0.274 M and λ = 453 nm, the rate equation for the oxidation of Ti(H₂O), ₆³⁺ by bromine was found to be: −d/[Br₂]T/dt=kK/[Br₂][Ti^III]/[H⁺]+K+kK/[Br₃⁻][Ti^III]/[H⁺+K, where k = 9.2 × 10⁻³ M ⁻¹ s ⁻¹ and K = 4.5 × 10⁻³ M. At [H⁺] = 1.0 M, [Br⁻] = 0.05–0.4 M, the apparent second-order rate constant decreases as [Br⁻] increases.

The pH-dependence of the oxidation of Ti^III-edta by bromine is interpreted in terms of the change in identity of the Ti^III-edta species as the pH of the reaction medium changes. The second-order rate constants were fitted using a non-linear least-square computer program with (1/k₀^edta)² weighting into an equation of the form: k₀^edta =k₁+k₂K₁[H⁺]⁻¹+k₃K₁K₂[H⁺]^−2/1+K₁[H⁺[H⁺⁻¹+K₁K₂[H⁺]⁻², with K₁ and K₂ fixed as earlier determined at 9.55 × 10⁻³ and 2.29 × 10⁻⁹ M, respectively, for the oxidation of bromine. k₁=k₂=(3.1±0.32)×10³M⁻¹s⁻¹ k₃=(2.3±0.45)×10⁶N⁻¹s⁻¹.

It is proposed that these electron transfer reactions proceed by univalent changes with the production of Br₂^.− as a transient intermediate. An outer-sphere mechanism is proposed for these reactions. The homonuclear exchange rate for Ti^III-edta+Ti^IV-edta is estimated at 32 M⁻¹ s⁻¹.