Decorrelation of a class of Gibbs particle processes and asymptotic properties of U-statistics

We study a stationary Gibbs particle process with deterministically bounded particles on Euclidean space defined in terms of an activity parameter and non-negative interaction potentials of finite range. Using disagreement percolation, we prove exponential decay of the correlation functions, provided a dominating Boolean model is subcritical. We also prove this property for the weighted moments of a U-statistic of the process. Under the assumption of a suitable lower bound on the variance, this implies a central limit theorem for such U-statistics of the Gibbs particle process. A by-product of our approach is a new uniqueness result for Gibbs particle processes.

Determination of Boolean models by densities of mixed volumes

In Weil (2001) formulae were proved for stationary Boolean models Z in ℝd with convex or polyconvex grains, which express the densities (specific mean values) of mixed volumes of Z in terms of related mean values of the underlying Poisson particle process X. These formulae were then used to show that in dimensions 2 and 3 the densities of mixed volumes of Z determine the intensity γ of X. For d = 4, a corresponding result was also stated, but the proof given was incomplete, since in the formula for the density of the Euler characteristic V̅0(Z) of Z a term $\overline V^{(0)}_{2,2}(X,X)$ was missing. This was pointed out in Goodey and Weil (2002), where it was also explained that a new decomposition result for mixed volumes and mixed translative functionals would be needed to complete the proof. Such a general decomposition result has recently been proved by Hug, Rataj, and Weil (2013), (2018) and is based on flag measures of the convex bodies involved. Here, we show that such flag representations not only lead to a correct derivation of the four-dimensional result, but even yield a corresponding uniqueness theorem in all dimensions. In the proof of the latter we make use of Alesker’s representation theorem for translation invariant valuations. We also discuss which shape information can be obtained in this way and comment on the situation in the nonstationary case.

p-Channel and n-Channel Thin-Film-Transistor Operation on Sprayed ZnO Nanoparticle Layers

Both n-channel and p-channel thin-film transistors have been realized on ZnO nanoparticle (NP) layers sprayed onto quartz substrates. In this study, nitrogen-doped ZnO-NPs were synthesized using an arc-discharge-mediated gas-evaporation method that was recently developed. Sprayed NP layers were characterized by scanning electron microscopy and Hall effect measurements. It was confirmed that p-type behaving NP layers can be obtained using ZnO-NPs synthesized with lower chamber pressure, whereas n-type conductivity can be obtained with higher chamber pressure. pn-junction diodes were also tested, resulting in clear rectifying characteristics. The possibility of particle-process-based ZnO-NP electronics was confirmed.

Fluid Flow and Defect Density Considerations when Drying Bumped Wafers Using Spin and Surface Tension Gradient Methods

Spin rinse drying (SRD) and surface tension gradient drying (STG) are used to clean and dry wafers after wet processing. These methods are effective at removing surface fluid and fluid trapped by capillary forces in small (<1um) features. SRD and STG processes combine driven fluid flows with controlled evaporation of thin water films to leave a dry wafer with low defect density (i.e. a low number of physical particle process adders, or areas of haze or oxidation).