Ni reactions with surfaces: dependence of gettering efficiencies for Ni on crystal-growth conditions, back-side-gettering techniques, oxygen precipitates and thermal treatments

We have performed measurements on the gettering efficiencies for Ni in different silicon wafers. Gettering efficiencies were measured of wafers grown by different crystal-growth techniques, such as Czochralski-grown (CZ) and floating zone (FZ), as well as wafers containing crystal-originated particles (COPs) of different size and density. Lightly boron doped CZ wafers covered with an epitaxial layer were also evaluated. In another set of experiments, we compared different back-side-gettering techniques, like poly-silicon, stacking faults and He-implanted back sides and the dependence of back-side gettering on cooling rate and contamination level. Internal surfaces of oxygen precipitates were also investigated. The gettering test started with a reproducible spin-on contamination in the range around 10¹² atoms/cm² and was followed by a thermal treatment to redistribute the Ni impurity in the wafer. Subsequently, wafers were analyzed for their surface and bulk contamination by a novel layer-by-layer etching, stratigraphical technique in combination with inductively coupled plasma mass spectrometry. No detectable gettering effect of COPs was found. FZ wafers differed remarkably in their gettering behavior from CZ wafers, obviously due to differences in aggregated self-point defects. Most remarkably, the deposition process of an epitaxial layer changed the gettering behavior of p/p- wafers. Comparing the gettering efficiencies of different back sides, an extraordinarily high gettering efficiency of He-implanted voids can be anticipated, which was higher than the gettering efficiency of poly-silicon and stacking faults. High cooling rates at the end of the drive-in cycle and low contamination levels lowered the gettering efficiencies of back-side-gettering techniques, suggesting a diffusion-limited gettering process. Based on the dependence of the gettering efficiencies on different drive-in cycles, a surface reaction as a mechanistic initiation of the drive-in must be assumed. Oxygen precipitates exhibited a high gettering effect for Ni contamination. All experimental results are interpreted by available active surfaces in the gettering phases. Received: 30 May 2001 / Accepted: 16 June 2001 / Published online: 30 August 2001     

Benchmark calculations of proton affinities and gas-phase basicities of molecules important in the study of biological phosphoryl transfer

Benchmark calculations of proton affinities and gas-phase basicities of molecules most relevant to biological phosphoryl transfer reactions are presented and compared with available experimental results. The accuracy of proton affinity and gas-phase basicity results obtained from several multi-level model chemistries (CBS-QB3, G3B3, and G3MP2B3) and density-functional quantum models (PBE0, B1B95, and B3LYP) are assessed and compared. From these data, a set of empirical bond enthalpy, entropy, and free energy corrections are introduced that considerably improve the accuracy and predictive capability of the methods. These corrections are applied to the prediction of proton affinity and gas-phase basicity values of important biological phosphates and phosphoranes for which experimental data does not currently exist. Comparison is made with results from semiempirical quantum models that are commonly employed in hybrid quantum mechanical/molecular mechanical simulations. Data suggest that the design of improved semiempirical quantum models with increased accuracy for relative proton affinity values is necessary to obtain quantitative accuracy for phosphoryl transfer reactions in solution, enzymes, and ribozymes.     

ARC-length method for differential equations

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MeV-boron implanted layer, oxygen precipitates and poly-silicon back side combined in one silicon wafer: at what defect will Cu and Ni be gettered?

We have measured the gettering efficiencies for Cu and Ni of various silicon wafers, such as MeV-boron-implanted p- polished wafers treated with two different implantation doses of 3×10¹³ atoms/cm² B and 1×10¹⁵ atoms/cm² B, respectively. A third kind of wafer was covered with a poly-silicon back side and thermally pretreated before the gettering test to form oxygen precipitates in the bulk. The gettering test started with a reproducible spin-on spiking on the front side of the wafers in the range around 10¹² atoms/cm², followed by a thermal treatment to redistribute the metallic impurities in the wafer. Then the gettering efficiencies were measured by a novel wet chemical layer-by-layer etching technique in combination with inductively coupled plasma mass spectrometry. This led to “stratigraphical concentration profiles” of the metallic impurities in the wafer with typical detection limits of (5–10)×10¹² atoms/cm³. The concentration profiles were compared with concentration profiles found after testing the gettering efficiency of p/p+ epitaxial wafers. Almost 100% of the total intentional Cu spiking was recovered in the boron buried layer for both implantation doses. On the front surface and in the region between the front surface and the buried layer a Cu concentration ∼20 times higher than on/in p/p+ epitaxial wafers/layers was measured for the implanted specimen. The lower implantation dose led to higher Cu-concentration levels on the front surface compared to the higher implantation dose. The wafer containing a MeV-boron-implanted layer as well as oxygen precipitates and a poly-silicon back side exhibited a Cu distribution of 30/∼0/70%, respectively. Thus, the gettering by poly-silicon exceeded both the gettering effects by the buried layer and by the oxygen precipitates. Ni gettering in MeV-boron-implanted wafers exhibited other characteristics. The gettering efficiency of the buried layer was 65%, while the remaining Ni contamination was equally distributed between the front-side region and the wafer back side. A wafer containing a buried layer obtained by a 1×10¹⁵ atoms/cm³ B dose and oxygen precipitates exhibited 17% of the total Ni contamination in the boron layer, while ∼80% of the total Ni contamination was gettered by oxygen precipitates. In the case of buried layer/oxygen precipitates/poly-silicon back side the distribution was found to be 13/37/45%, thus exhibiting equal gettering strengths for oxygen precipitates and the poly-silicon back side for Ni contamination. The results were discussed in terms of segregation and relaxation-induced gettering mechanisms including different reaction rates. Received: 30 May 2001 / Accepted: 16 June 2001 / Published online: 30 August 2001     

Pair formation and global ordering of strongly interacting ferrocolloid mixtures: an integral equation study

Using the reference hypernetted chain (RHNC) integral equation theory and an accompanying stability analysis we investigate the structural and phase behaviors of model bidisperse ferrocolloids based on correlations of the homogeneous isotropic high-temperature phase. Our model consists of two species of dipolar hard spheres (DHSs) which dipole moments are proportional to the particle volume. At small packing fractions our results indicate the onset of chain formation, where the (more strongly coupled) A species behaves essentially as a one-component DHS fluid in a background of B particles. At high packing fractions, on the other hand, the RHNC theory indicates the appearance of isotropic-to-ferromagnetic transitions (volume ratios close to one) and demixing transitions (smaller volume ratios). However, contrary with the related case of monodisperse DHS mixtures previously studied by us [Phys. Rev. E 70, 031201 (2004)], none of the present bidisperse systems exhibit demixing within the isotropic phase, rather we observe coupled ferromagnetic/demixing phase transitions.     

On Hölder and BMO estimates for \bar \partial on convex domains in C2on convex domains in C2

We prove that on convex domains in C² a suitable integral solution operator for the Cauchy-Riemann equations preserves exact Hölder regularity, and that it maps bounded (0,1) forms into BMO with respect to volume measure.