Thomas Wieder

Microstructure analysis of ohmic contacts on MBE grown n-GaSb and investigation of sub-micron contacts

We investigated the thermally induced solid state interdiffusion of Au Ge Pd and Ge Pd ohmic contacts on MBE grown n-GaSb. Furthermore, the electrical behavior of these contacts for different contact sizes down to 540 nm in diameter was compared. A specific contact resistivity as low as 4.9 × 10 6 Ωcm 2 was measured for the Au/Ge/Pd metallization. After annealing, polycrystalline AuSb 2 was observed by grazing incident X-ray diffraction (GIXD). Compared to Ge/Pd metallizations a gold top layer reduces the specific contact resistivity. The atomic structure or microstructure of the Au/Ge/Pd metallization showed a significant reduction of the thickness of amorphous Ge and led to a more spiky interface, which was observed by cross-sectional transmission clectron microscopy (TEM). Furthermore, an epitaxial regrowth of GaSb occurs, which is estimated to lead to a n - GaSb layer. The atomic microstructure has a significant effect on the current voltage (I V) characteristic up to a contact size of 950 nm in diameter, which shows a wide spread from ohmic to a more Schottky like behavior.

Grazing excidence diffraction versus grazing incidence diffraction for strain/stress evaluation in thin films

The reflection shift δ2Θ caused by a radial shift δ r of the sample away from its tangential position at the focusing circle is examined for grazing incidence diffraction and grazing excidence diffraction. Experimental results for residual strain/stress evaluation on thin films using a Bragg–Brentano diffractometer with a grazing incidence equipment are presented. Grazing excidence diffraction is less sensitive to δ r than grazing incidence diffraction.

The Number of Hierarchical Orderings

An ordered set-partition (or preferential arrangement) of n labeled elements represents a single “hierarchy” these are enumerated by the ordered Bell numbers. In this note we determine the number of “hierarchical orderings” or “societies”, where the n elements are first partitioned into m ≤ n subsets and a hierarchy is specified for each subset. We also consider the unlabeled case, where the ordered Bell numbers are replaced by the composition numbers. If there is only a single hierarchy, we show that the average rank of an element is asymptotic to n/(4 log 2) in the labeled case and to n/4 in the unlabeled case.

Phonon dispersion and elastic constants in Fe-Cr-Mn-Ni austenitic steel

The lattice dynamics of Fe-18Cr-10Mn-16Ni austenitic steel was studied by inelastic neutron scattering techniques. Phonon dispersion curves were measured in the [100], [011] and [111] directions at low wavevectors. The measured dispersion curves are similar to those of the γ-Fe and the Fe0.75Ni0.25 alloy, but do not show the anomalous concave curvature of the T1 [001] branch at lower wave vectors as characteristic for γ-Fe. All available data were used for the evaluation of the atomic force constants, elastic constants and engineering elastic moduli of Fe-18Cr-10Mn-16Ni steel.

Surface Wave Propagation in Thin Silver Films under Residual Stress

Investigations using surface acoustic waves provide information on the elastic properties of thin films. Residual stresses change the phase velocity of the surface waves. We have calculated the phase velocity and dispersion of surface waves in thin silver films with a strong [111]-fibre texture. A non-linear description of surface waves propagating along the [110]-direction of the substrate has been developed on the basis of an acoustoelastic theory, taking into account residual stresses. The relative change Δc/c of the velocity v was found to be linear for large excitation frequencies. The dispersion curves were measured using a photoacoustic method. For sputtered polycrystalline thin silver films we found good agreement between the experimental and calculated dispersion curves for frequencies up to 225 MHz

A GENERALIZED DEBYE SCATTERING FORMULA AND THE HANKEL TRANSFORM

Abstract The diffracted intensity of an x-ray or neutron diffraction experiment is expressed as an integral over an atomic position distribution function. A generalized Debye scattering formula results. Since this distribution function is expanded into a series of spherical harmonics, an inverse Hankel transform of the intensity allows the calculation of the expansion coefficients which describe the atomic arrangement completely. The connections between the generalized Debye scattering formula and the original Debye formula as well as the Laue scattering formula are derived.

New scattering formula for the analysis of X-ray line broadening by composition profiles

The variation of the lattice constantsai(i=1,2,3) with the depthR in a crystalline solid leads to broadening of the x-ray reflections. The broadening is calculated for polycrystalline samples, where the lattice constant profileai(R) extends over several grain diameters. The calculation is performed by superimposing, in kinematical theory, the waves scattered from the lattice planes with varying distances and taking into account the absorption of the x-rays in the material.

Yield stress increase in a W/Cu composite observed by neutron diffraction

Ceramic matrix composites with a ductile reinforcement phase can be produced by infiltrating a metal melt into a porous ceramic preform [1, 2]. Due to the thermal expansion mismatch, residual stresses of opposite signs develop in the ceramic and metal phase. For alumina/aluminum composites, the tensile stresses of the metal phase can exceed several times its bulk yield stress [3, 4]. This phenomenon may be called “yield stress increase” and was first observed in mechanically constrained metal wires by Ashby et al. [5]. The magnitude of the yield strength increase depends on the diameter of the ductile ligaments, their shape and connectivity [3]. In this study, exceptionally high residual stresses have been observed in the copper phase of a tungsten/copper composite with a graded interpenetrating network microstructure. These stresses are about 16 times larger than the yield stress of bulk, age-hardened copper. The graded W/Cu composite was produced from tungsten powder containing 2 wt % Ni. From this powder, a body of 57% relative density and an average grain size of 14 μm was produced by partial sintering. The porosity was locally increased by anodic oxidation in 2 M NaOH at 8.5 mA cm−2 for 165 h [6]. The resulting tungsten preform with a graded porosity was infiltrated with molten electrolyte copper at 1250 ◦C in a hydrogen atmosphere for 1/2 h. After cooling to room temperature, a composite with a gradient in the copper content along one direction (called depth) was obtained (see Fig. 1). The composite was dense. Determination of Young’s modulus of the composites and phase contrast acoustic microscopy both indicate that no microcracks were present at the tungsten/copper interfaces. Image analysis of optical micrographs showed a gradient in copper content from 49 to 66 vol % (Fig. 2). The electrochemical process also introduces a gradient in the specific interface area into the composite.1 The specific interface area is a measure of the thickness of the average copper ligaments and hence the mechanical constraint exerted on the copper phase. The copper-rich region of the graded composite had a specific interface area of 0.13 μm−1 whereas the region of low copper content had a specific interface area of 0.33 μm−1. Assuming cylindrical copper ligaments of uniform diameter, one calculates copper ligament diameters between 30 and 12 μm. Neutron diffraction allows one to determine the stress tensor in the tungsten and copper phase σ = σ (z) as a function of depth z by selecting the probe volume using appropriate beam collimators. The present measurements were done using the D1A diffractometer at the Institute Laue-Langevin (ILL), Grenoble. D1A is equipped with a long scattered beam collimator resulting in a probe volume of ≈1 mm3 [7]. The measured strain 2= 2(h k l, φ, ω, z) depends on the measurement direction (φ, ω) with respect to the sample coordinate system. Furthermore, 2 depends on z because of the copper concentration gradient. Copper is an elastically anisotropic material, therefore 2= 2(h k l, φ, ω, z) also depends on the lattice plane indices (h k l). To account for the anisotropy, we measured the Cu(1 1 1)and the Cu(3 1 1)-reflection of copper. The diffraction experiments on three samples showed that the copper phase is textured and can be regarded as one single crystal. This texture results from the solidification process, when the solidification front takes on one single crystallographic orientation. Because of the texture, we had to search for suitable sets of tilting angles (φ, ω) to record measurable intensities [8]. Because tungsten is elastically isotropic, we worked with the W(1 1 1)-reflection only. From the measured 2(h k l, φ, ω), the stress tensor σ (z) was calculated at all selected z-values according to Hooke’s law [9]. Single-crystal elastic compliances were used, because the probed volume consisted essentially of a single crystal.2 Fig. 3 shows for both phases the three components σ11, σ22 and σ33 of σ (z) expressed in the principal axes system. For copper, the stress is relaxed at the surface where the copper concentration is highest. At great depths (z<−3 mm), where the copper concentration goes to zero, tensile stress exists, and in the intermediate region compressive stress is present. The tungsten phase has stresses with opposite depth dependence. At the free surface, where the tungsten concentration was low, tensile stress is found. In the intermediate region, tensile stress still exists, which drops to zero at great depths, where the tungsten concentration rises to 100%. This observed depth dependence can be qualitatively explained by the mechanical equilibrium conditions and the lever rule for stresses in a two-phase material.3 At any depth z, the concentration-weighted stresses in both phases balance each other (as long as no interface failure occurs). Stresses at different depths z