scholarly journals Energy stability and error estimates of exponential time differencing schemes for the epitaxial growth model without slope selection

2017 ◽  
Vol 87 (312) ◽  
pp. 1859-1885 ◽  
Author(s):  
Lili Ju ◽  
Xiao Li ◽  
Zhonghua Qiao ◽  
Hui Zhang
Keyword(s):  
Epitaxial Growth ◽  
Error Estimates ◽  
Growth Model ◽  
Energy Stability ◽  
Exponential Time ◽  
Exponential Time Differencing ◽  
Slope Selection

scholarly journals A stabilized second order exponential time differencing multistep method for thin film growth model without slope selection

2020 ◽  
Vol 54 (3) ◽  
pp. 727-750 ◽  
Author(s):  
Wenbin Chen ◽  
Weijia Li ◽  
Zhiwen Luo ◽  
Cheng Wang ◽  
Xiaoming Wang
Keyword(s):  
Thin Film ◽  
Growth Model ◽  
Film Growth ◽  
Multistep Method ◽  
Second Order ◽  
Thin Film Growth ◽  
Energy Stability ◽  
Exponential Time ◽  
Exponential Time Differencing ◽  
Slope Selection

In this paper, a stabilized second order in time accurate linear exponential time differencing (ETD) scheme for the no-slope-selection thin film growth model is presented. An artificial stabilizing term $ A{\tau }^2\frac{\mathrm{\partial }{\Delta }^2u}{\mathrm{\partial }t}$ is added to the physical model to achieve energy stability, with ETD-based multi-step approximations and Fourier collocation spectral method applied in the time integral and spatial discretization of the evolution equation, respectively. Long time energy stability and detailed 𝓁∞(0,T;𝓁2) error analysis are provided based on the energy method, with a careful estimate of the aliasing error. In addition, numerical experiments are presented to demonstrate the energy decay and convergence rate.

scholarly journals Exponential time differencing based efficient SC-PML for RCS simulation

2020 ◽  
Vol 31 (4) ◽  
pp. 703-711 ◽  
Author(s):  
Niu Liqiang ◽  
Xie Yongjun ◽  
Jiang Haolin ◽  
Wu Peiyu
Keyword(s):  
Exponential Time ◽  
Exponential Time Differencing

Epitaxial Growth Following Crystal Nucleation in Laser-Quenched Si Films on SiO2

2015 ◽  
Vol 1770 ◽  
pp. 67-72
Author(s):  
Vernon K. Wong ◽  
A. M. Chitu ◽  
A. B. Limanov ◽  
James S. Im
Keyword(s):  
Epitaxial Growth ◽  
Growth Model ◽  
Crystal Nucleation ◽  
Key Factors ◽  
Complete Melting ◽  
Melting Regime ◽  
Direct Growth ◽  
Crystal Core ◽  
Excimer Laser Irradiation ◽  
Si Films

ABSTRACTWe have investigated the solidified microstructure of nucleation-generated grains obtained via complete melting of Si films on SiO2 at high nucleation temperatures. This was achieved using a high-temperature-capable hot stage in conjunction with excimer laser irradiation. As predicted by the direct-growth model that considers (1) the evolution in the temperature of the solidifying interface and (2) the subsequent modes of growth (consisting of amorphous, defective, and epitaxial) as key factors, we were able to observe the appearance of “normal” grains that possess a single-crystal core area. These grains, which are in contrast to previously reported flower-shaped grains that fully make up the microstructure of the solidified films obtained via irradiation at lower preheating temperatures (and amongst which these “normal” grains emerge), indicate that epitaxial growth of nucleated crystals must have taken place within the grains. We discuss the implications of our findings regarding (1) the validity of the direct-growth model, (2) the nature of the heterogeneous nucleation mechanism, and (3) the alternative explanations and assumptions that have been previously employed in order to explain the microstructure of Si films obtained via nucleation and growth within the complete melting regime.

scholarly journals Exponential-time differencing schemes for low-mass DPD systems

2014 ◽  
Vol 185 (1) ◽  
pp. 229-235 ◽  
Author(s):  
N. Phan-Thien ◽  
N. Mai-Duy ◽  
D. Pan ◽  
B.C. Khoo
Keyword(s):  
Exponential Time ◽  
Exponential Time Differencing ◽  
Low Mass
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