Island-size distribution and capture numbers in three-dimensional nucleation: Dependence on island morphology

2009 ◽  
Vol 80 (4) ◽  
Author(s):  
John Royston ◽  
Jacques G. Amar
Keyword(s):  
Size Distribution ◽  
Three Dimensional ◽  
Island Size

Effect Of Phosphorus On Ge/Si(001) Island Formation

2002 ◽  
Vol 737 ◽  
Author(s):  
Theodore I. Kamins ◽  
Gilberto Medeiros-Ribeiro ◽  
Douglas A. A. Ohlberg ◽  
R. Stanley Williams
Keyword(s):  
Deposition Rate ◽  
Strain Energy ◽  
Competitive Adsorption ◽  
Lattice Mismatch ◽  
Three Dimensional ◽  
Deposition Process ◽  
Thin Layers ◽  
Island Size ◽  
Partial Pressures ◽  
Intermediate Size

ABSTRACTWhen Ge is deposited epitaxially on Si, the strain energy from the lattice mismatch causes the Ge in layers thicker than about four monolayers to form distinctive, three-dimensional islands. The shape of the islands is determined by the energies of the surface facets, facet edges, and interfaces. When phosphorus is added during the deposition, the surface energies change, modifying the island shapes and sizes, as well as the deposition process. When phosphine is introduced to the germane/hydrogen ambient during Ge deposition, the deposition rate decreases because of competitive adsorption. The steady-state deposition rate is not reached for thin layers. The deposited, doped layers contain three different island shapes, as do undoped layers; however, the island size for each shape is smaller for the doped layers than for the corresponding undoped layers. The intermediate-size islands are the most significant; the intermediate-size doped islands are of the same family as the undoped, multifaceted “dome” structures, but are considerably smaller. The largest doped islands appear to be related to the defective “superdomes” discussed for undoped islands. The distribution between the different island shapes depends on the phosphine partial pressure. At higher partial pressures, the smaller structures are absent. Phosphorus appears to act as a mild surfactant, suppressing small islands.

scholarly journals Derivation of Equations for a Size Distribution of Spherical Particles in Non-Transparent Materials

2021 ◽  
Vol 5 (4) ◽  
pp. 53-60
Author(s):  
Daniel Gurgul ◽  
Andriy Burbelko ◽  
Tomasz Wiktor
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Size Distribution ◽  
Density Function ◽  
Cross Section ◽  
Three Dimensional ◽  
Spherical Particles ◽  
Two Dimensional ◽  
Mathematical Formulas ◽  
Transparent Materials

This paper presents a new proposition on how to derive mathematical formulas that describe an unknown Probability Density Function (PDF3) of the spherical radii (r3) of particles randomly placed in non-transparent materials. We have presented two attempts here, both of which are based on data collected from a random planar cross-section passed through space containing three-dimensional nodules. The first attempt uses a Probability Density Function (PDF2) the form of which is experimentally obtained on the basis of a set containing two-dimensional radii (r2). These radii are produced by an intersection of the space by a random plane. In turn, the second solution also uses an experimentally obtained Probability Density Function (PDF1). But the form of PDF1 has been created on the basis of a set containing chord lengths collected from a cross-section.The most important finding presented in this paper is the conclusion that if the PDF1 has proportional scopes, the PDF3 must have a constant value in these scopes. This fact allows stating that there are no nodules in the sample space that have particular radii belonging to the proportional ranges the PDF1.

scholarly journals Experimental investigation on pore size distribution and drying kinetics during lyophilization of sugar solutions

2018 ◽  
Author(s):  
Petra Foerst ◽  
M. Lechner ◽  
N. Vorhauer ◽  
H. Schuchmann ◽  
E. Tsotsas
Keyword(s):  
Pore Structure ◽  
Pore Size Distribution ◽  
Pore Size ◽  
Size Distribution ◽  
Freeze Drying ◽  
Three Dimensional ◽  
Drying Kinetics ◽  
Process Efficiency ◽  
Freeze Dried ◽  
Pore Size Distributions

The pore structure is a decisive factor for the process efficiency and product quality of freeze dried products. In this work the two-dimensional ice crystal structure was investigated for maltodextrin solutions with different concentrations by a freeze drying microscope. The resulting drying kinetics was investigated for different pore structures. Additionally the three-dimensional pore structure of the freeze dried samples was measured by µ-computed tomography and the pore size distribution was quantified by image analysis techniques. The two- and three-dimensional pore size distributions were compared and linked to the drying kinetics.Keywords: pore size distribution; freeze drying; maltodextrin solution; freeze drying microscope   

Spatial Correlations in Growing Films

2000 ◽  
Vol 619 ◽  
Author(s):  
M.C. Bartelt
Keyword(s):  
Size Distribution ◽  
Lattice Gas ◽  
Mean Field ◽  
Film Deposition ◽  
Nucleation Theory ◽  
Spatial Correlations ◽  
Island Size ◽  
Pit Formation ◽  
Free Region ◽  
Lattice Gas Models

ABSTRACTDetailed analyses of non-equilibrium lattice-gas models of island nucleation and growth during film deposition (or etching) have been invaluable in elucidating basic issues in nucleation theory, deviations from mean-field predictions, and experimental observations. Particularly interesting and useful is the behavior of spatial correlations in the adlayer which develop during island (or pit) formation. In particular, a strong depletion in the population of island pairs at separations smaller than the average follows from depletion in the density of diffusing adspecies near islands. This feature delays percolation of clusters of coalesced islands. Another recently discovered and more subtle feature is a strong correlation between the width of the island-free region surrounding an island and the size and growth rate of that island. This direct correlation between island sizes and separations controls the shape of the island size distribution. If incorporated into rate-equation descriptions, it recovers the exact form of the scaling function for the island size distribution.

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