Development of the Grain Size Distribution During the Crystallization of an Amorphous Solid

2011 ◽  
Vol 1308 ◽  
Author(s):  
Andreas Bill ◽  
Ralf B. Bergmann
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Growth Rates ◽  
Amorphous Solid ◽  
Amorphous Solids ◽  
Nucleation And Growth ◽  
Analytic Description ◽  
Silicon Thin Films ◽  
Random Nucleation

ABSTRACTWe present an overview of the theory developed over the last few years to describe the crystallization of amorphous solids. The microstructure of the crystallizing solid is described in terms of the grain size distribution (GSD). We propose a partial differential equation that captures the physics of crystallization in random nucleation and growth processes. The analytic description is derived for isotropic and anisotropic growth rates and allows for the analysis of different stages of crystallization, from early to full crystallization. We show how the timedependence of effective nucleation and growth rates affect the final distribution. In particular, we demonstrate that for cases described by the Kolmogorov-Avrami-Mehl-Johnson (KAMJ) model applicable to a large class of crystallization processes a lognormal type distribution is obtained at full crystallization. The application of the theory to the crystallization of silicon thin films is discussed.

Modeling the Grain Size Distribution during Solid Phase Crystallization of Silicon

2009 ◽  
Vol 1153 ◽  
Author(s):  
Andreas Bill ◽  
Anthony V Teran ◽  
Ralf B Bergmann
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Solid Phase ◽  
Good Description ◽  
Nucleation And Growth ◽  
Solid Phase Crystallization ◽  
Silicon Thin Films ◽  
Analytical Expressions ◽  
Physical Principles

AbstractWe analyze the grain size distribution during solid phase crystallization of Silicon thin films. We use a model developed recently that offers analytical expressions for the time-evolution of the grain size distribution during crystallization of a d-dimensional solid. Contrary to the usual fit of the experimental results with a lognormal distribution, the theory describes the data from basic physical principles such as nucleation and growth processes. The theory allows for a good description of the grain size distribution except for early stages of crystallization. The latter case is expected and discussed. An important outcome of the model is that the distribution at full crystallization is determined by the time-dependence of the nucleation and growth rates of grains. In the case under consideration, the theory leads to an analytical expression that has the form of a lognormal-type distribution for the fully crystallized sample.

Simulation of the Kinetics of Grain-Boundary Nucleated Phase Transformations

2011 ◽  
Vol 172-174 ◽  
pp. 1128-1133 ◽  
Author(s):  
Eric A. Jägle ◽  
Eric J. Mittemeijer
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Phase Transformations ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Kinetic Models ◽  
Micro Structure ◽  
Boundary Area ◽  
Random Nucleation ◽  
Kinetics Of

The kinetics of phase transformations for which nucleation occurs on parent-micro-structure grain boundaries, and the resulting microstructures, were investigated by means ofgeometric simulations. The influences of parent microstructure grain-boundary area density,parent grain-size distribution and parent→product kinetics were analysed. Additionally, thesimulated kinetics were compared with predictions from two kinetic models, namely a modelproposed for spatially random nucleation and a model proposed for grain-boundary nucleation.It was found that the simulated transformed fraction as function of time lies in between the twomodel predictions for all investigated parent microstructures and parent→product kinetics.

Deposition and Characterization of Polycrystalline Silicon Films on Glass for thin Film Solar Cells

1997 ◽  
Vol 467 ◽  
Author(s):  
R. B. Bergmann ◽  
J. Krinke ◽  
H. P. Strunk ◽  
J. H. Werner
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Solid Phase ◽  
Chemical Vapor ◽  
In Situ Monitoring ◽  
Random Nucleation ◽  
Amorphous Si ◽  
Log Normal ◽  
Polycrystalline Silicon Films

ABSTRACTWe deposit phosphorus-doped, amorphous Si by low pressure chemical vapor deposition and subsequently crystallize the films by furnace annealing at a temperature of 600°C. Optical in-situ monitoring allows one to control the crystallization process. Phosphorus doping leads to faster crystallization and a grain size enhancement with a maximum grain size of 15 μm. Using transmission electron microscopy we find a log-normal grain size distribution in our films. We demonstrate that this distribution not only arises from solid phase crystallization of amorphous Si but also from other crystallization processes based on random nucleation and growth. The log-normal grain size distribution seems to be a general feature of polycrystalline semiconductors.

The Grain Size Distribution in Crystallization Processes With Anisotropic Growth Rate

2010 ◽  
Vol 1245 ◽  
Author(s):  
Kimberly S. Lokovic ◽  
Ralf B. Bergmann ◽  
Andreas Bill
Keyword(s):  
Growth Rate ◽  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Amorphous Solid ◽  
Anisotropic Growth ◽  
Ellipsoidal Shape ◽  
Shape Invariant ◽  
Spherical Grains ◽  
Effective Growth

AbstractThe grain size distribution allows characterizing quantitatively the microstructure at different stages of crystallization of an amorphous solid. We propose a generalization of the theory we established for spherical grains, to the case of grains with ellipsoidal shape. We discuss different anisotropic growth mechanisms of the grains in thin films. An analytical expression of the grain size distribution is obtained for the case where grains grow through a change of volume while keeping their shape invariant. The resulting normalized grain size distribution is shown to be affected by anisotropy through the time-decay of the effective growth rate.

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