Engineering metal precipitate size distributions to enhance gettering in multicrystalline silicon

The extraction of metal impurities during phosphorus diffusion gettering (PDG) is one of the crucial process steps when fabricating high-efficiency solar cells using low-cost, lower-purity silicon wafers. In this work, we show that for a given metal concentration, the size and density of metal silicide precipitates strongly influences the gettering efficacy. Different precipitate size distributions can be already found in silicon wafers grown by different techniques. In our experiment, however, the as-grown distribution of precipitated metals in multicrystalline Si sister wafers is engineered through different annealing treatments in order to control for the concentration and distribution of other defects. A high density of small precipitates is formed during a homogenization step, and a lower density of larger precipitates is formed during extended annealing at 740º C. After PDG, homogenized samples show a decreased interstitial iron concentration compared to as-grown and ripened samples, in agreement with simulations.

Fractal parameters of pore space from CT images of soils under contrasting management practices

Soil structure plays an important role in flow and transport phenomena, and a quantitative characterization of the spatial heterogeneity of the pore space geometry is beneficial for prediction of soil physical properties. Morphological features such as pore-size distribution, pore space volume or pore?solid surface can be altered by different soil management practices. Irregularity of these features and their changes can be described using fractal geometry. In this study, we focus primarily on the characterization of soil pore space as a 3D geometrical shape by fractal analysis and on the ability of fractal dimensions to differentiate between two a priori different soil structures. We analyze X-ray computed tomography (CT) images of soils samples from two nearby areas with contrasting management practices. Within these two different soil systems, samples were collected from three depths. Fractal dimensions of the pore-size distributions were different depending on soil use and averaged values also differed at each depth. Fractal dimensions of the volume and surface of the pore space were lower in the tilled soil than in the natural soil but their standard deviations were higher in the former as compared to the latter. Also, it was observed that soil use was a factor that had a statistically significant effect on fractal parameters. Fractal parameters provide useful complementary information about changes in soil structure due to changes in soil management. Read More: http://www.worldscientific.com/doi/abs/10.1142/S0218348X14400118?queryID=%24%7BresultBean.queryID%7D&

Computer Simulation of Packing of Particles with Size Distributions Produced by Fragmentation Processes

Fragmentation schemes inspired by theoretical results and conjectures of Kolmogorov are applied to produce particle size distributions of different natures, depending on fragmentation parameters. A two-dimensional computer simulation method of packing is applied to the resulting distributions and the void fraction is evaluated. The relationship between the void fraction and characteristic parameters of the fragmentation process is studied.

Computer simulation of packing of particles with size distributions produced by fragmentation processes

Fragmentation schemes inspired by theoretical results and conjectures of Kolmogorov are applied to produce particle size distributions of different natures, depending on fragmentation parameters. A two-dimensional computer simulation method of packing is applied to the resulting distributions and the void fraction is evaluated. The relationship between the void fraction and characteristic parameters of the fragmentation process is studied.

Application of density functional theory to analysis of energetic heterogeneity and pore size distribution of activated carbons

A new approach based on the nonlocal density functional theory to determine pore size distribution (PSD) of activated carbons and energetic heterogeneity of the pore wall is proposed. The energetic heterogeneity is modeled with an energy distribution function (EDF), describing the distribution of solid-fluid potential well depth (this distribution is a Dirac delta function for an energetic homogeneous surface). The approach allows simultaneous determining of the PSD (assuming slit shape) and EDF from nitrogen or argon isotherms at their respective boiling points by using a set of local isotherms calculated for a range of pore widths and solid-fluid potential well depths. It is found that the structure of the pore wall surface significantly differs from that of graphitized carbon black. This could be attributed to defects in the crystalline structure of the surface, active oxide centers, finite size of the pore walls (in either wall thickness or pore length), and so forth. Those factors depend on the precursor and the process of carbonization and activation and hence provide a fingerprint for each adsorbent. The approach allows very accurate correlation of the experimental adsorption isotherm and leads to PSDs that are simpler and more realistic than those obtained with the original nonlocal density functional theory.

Adsorption in slit pores and pore-size distribution: A molecular layer structure theory

A new approach is developed to analyze the thermodynamic properties of a sub-critical fluid adsorbed in a slit pore of activated carbon. The approach is based on a representation that an adsorbed fluid forms an ordered structure close to a smoothed solid surface. This ordered structure is modelled as a collection of parallel molecular layers. Such a structure allows us to express the Helmholtz free energy of a molecular layer as the sum of the intrinsic Helmholtz free energy specific to that layer and the potential energy of interaction of that layer with all other layers and the solid surface. The intrinsic Helmholtz free energy of a molecular layer is a function (at given temperature) of its two-dimensional density and it can be readily obtained from bulk-phase properties, while the interlayer potential energy interaction is determined by using the 10-4 Lennard-Jones potential. The positions of all layers close to the graphite surface or in a slit pore are considered to correspond to the minimum of the potential energy of the system. This model has led to accurate predictions of nitrogen and argon adsorption on carbon black at their normal boiling points. In the case of adsorption in slit pores, local isotherms are determined from the minimization of the grand potential. The model provides a reasonable description of the 0-1 monolayer transition, phase transition and packing effect. The adsorption of nitrogen at 77.35 K and argon at 87.29 K on activated carbons is analyzed to illustrate the potential of this theory, and the derived pore-size distribution is compared favourably with that obtained by the Density Functional Theory (DFT). The model is less time-consuming than methods such as the DFT and Monte-Carlo simulation, and most importantly it can be readily extended to the adsorption of mixtures and capillary condensation phenomena.

Pore size distribution analysis of activated carbons: Application of density functional theory using nongraphitized carbon black as a reference system

The application of nonlocal density functional theory (NLDFT) to determine pore size distribution (PSD) of activated carbons using a nongraphitized carbon black, instead of graphitized thermal carbon black, as a reference system is explored. We show that in this case nitrogen and argon adsorption isotherms in activated carbons are precisely correlated by the theory, and such an excellent correlation would never be possible if the pore wall surface was assumed to be identical to that of graphitized carbon black. It suggests that pore wall surfaces of activated carbon are closer to that of amorphous solids because of defects of crystalline lattice, finite pore length, and the presence of active centers.. etc. Application of the NLDFT adapted to amorphous solids resulted in quantitative description of N-2 and Ar adsorption isotherms on nongraphitized carbon black BP280 at their respective boiling points. In the present paper we determined solid-fluid potentials from experimental adsorption isotherms on nongraphitized carbon black and subsequently used those potentials to model adsorption in slit pores and generate a corresponding set of local isotherms, which we used to determine the PSD functions of different activated carbons. (c) 2005 Elsevier Ltd. All rights reserved.