Visualization of Large-scale Atomic During the Melting and … · 2019. 8. 1. · VLSIDESIGN 2001,...

VLSI DESIGN2001, Vol. 13, Nos. 1-4, pp. 269-271Reprints available directly from the publisherPhotocopying permitted by license only

(C) 2001 OPA (Overseas Publishers Association) N.V.Published by license under

the Gordon and Breach Science Publishers imprint,member of the Taylor & Francis Group.

Visualization of Large-scale Atomic InteractionsDuring the Melting and Crystallization Process

ROMAN I)URIKOVI(;*

Department of Computer Software, The University of Aizu, Aizu-Wakamatsu, Fukushima-ken 965-8580, Japan

Atomic-scale material model capable of melting, crystallization and amorphization hasbeen developed to examine the defect formation and crystal growth processes frommelted silicon (Si) based on the ordinary Langevin equations of motion. The developedcomputer system consists of simulation and visualization part. Simulation supports thelarge-scale molecular-dynamics (MD) clusters with solid/liquid interface respondinginteractively to the control parameters such as the temperature gradient and pullingspeed. Material behaviour simulation is limited to 10particle objects representingdifferent atoms. A particle in proposed dynamic system interacts through attractivecovalent forces and short-range repulsion forces in all three dimensions. This researchwas conducted to understand the processes that can control the quality of single-crystalSi grown from the melt by Czochralski crystal puller.

Keywords: Molecular dynamics; Si crystallization; Czochralski puller

INTRODUCTION

Although, defect formation can be hardly avoidedin Si technologies such as crystal growth frommelted Si, and thermal oxide growth, theirtopology as well as formation mechanism are notwell understood, because of high temperature andintensive reactivity of melt. Molecular dynamics(MD) is currently the only available method tohandle the large-scale simulations of solidificationfrom melted Si. Small molecular models (up to 100atoms) that may contain multiple types of atoms,can be created with a commercial quantummechanics package called Gausian94 [1]. This

package falls in to a group of ab initio methodswhen very accurate molecular orbital calculationsare carried out for the entire structure withhydrogen termination. Unfortunately, no suchsystem is available for larger molecular models.Over the years, much attention has been given in

the physics and chemistry literature to the devel-opment of discrete liquid models involving aggre-gate molecular dynamics in which the moleculesare subject to various interaction potentials, viz.Berendsen [2]. A basic technique is to model long-range attraction and short-range repulsion forcesbetween pairs of particles according to potentialsof the Lennard-Jones type, which lead to forces

*Tel.: (242) 456-7890, Fax: (321) 654-0987, e-mail: [email protected]

269

270 R. I)URIKOVI(

involving inverse powers of particle separationdistance as proposed by Tersoff [3]. RecentlyIshimaru et al. [4] demonstrated that interatomicpotential proposed by Tersoff is very good inreproduction of experimental results and in addi-tion to crystal Si simulations it can be used tosimulate both the amorphous and liquid state ofpure Si by different heating and freezing methodsof melted Si. This paper proposes the approach formodeling and visualization of large scale molecu-lar models applied on the simulation of a single-crystal silicon growth from molten silicon. Toprovide experimentalists with a familiar way oflooking at structure of simulation data, severaldiagnostic imaging techniques that aid the analy-sis of structure at atomic level such as radialdistribution function, bond angle distributionfunction, and static structure factors are proposedhere to be calculated from particle clusters ina run.

SIMULATION METHOD

In order to simulate the pulling motion of a crystalthe Langevin equation of motion should beslightly modified by introduction of a constantpulling speed ve, that is

mii/i(t) --mi’yivi(t) -k- Fi({x(t) ) -k- ei(t)i -[- c i (1)

where xi, i, and ,-)/i 5ps -1, are the position,velocity, atomic mass and friction coefficient of thei-th particle at time t, respectively. The inter-atomic force Fi between the N particles is derivedas variational derivative of the Tersoff [2] potentialfor Si, the stochastic force Ri was introduced tomimic the motion of solvent molecules on thesolute, it also serves as temperature controller inthe system. The use of Tersoff parameters for theSi and C type of molecules has some limitations inMD simulations as delineated by Halicionglu [5],however, they were taken into account in ourimplementations.

Concerning the nature of the stochastic force Riit is assumed to be stationary, Markovian andGaussian with zero mean and to have no correla-tion with initial velocities vi(0) nor with thesystematic force Fi(O). The stochastic numericalintegration of the third order proposed byGunsteren and Berendsen [6] was performed underthe constant volume within the cubic domain withperiodic boundary conditions on side faces and areflection plane on set at 2 ]k bellow the bottom ofthe volume. At each time step (0.002ps) thecollision between the particle and the reflectionplane is calculated to prevent particle fromescaping out of the simulation volume.

CRYSTAL GROWTH EXAMPLE

For MD simulation of crystal growth, a liquid-crystal interface was at first prepared by attachingcrystal sub-volume above the one with liquidatomic structure. Consequently, the system washeated at given temperature gradient along Z axisand crystal atoms were pulled with constant speedin Z direction for the simulation of crystal growth,see Figure 1. Figure 2 shows the simulated crystalgrowth process with a pulling speed of 5 m/s in the[111] direction. Joining two heated crystalline Sicells made initial states. The top cell had density ofcrystal Si, 2.33g/cm3 and the bottom had 2.57g/cm3, which gives the density of liquid Si structure.Calculated growth rate and pulling speed are muchlarger then in a real crystal puller because muchlarger volume and longer time period is needed to

Ca) (b)

FIGURE Simulation domain under consideration showingan initial liquid-crystal interface and temperature distributionalong the Z axis.

Si CRYSTALLIZATION 271

Z

pulling direction

solid-liquid300K interface

15K/A reflectionplane

large-scale systems. The advantages of the pro-posed dynamic model are in its application foranalysis and study of formation complexes ofsilicon defects where ab initio computations maybe prohibitively expensive, implementation ofadditional types of atoms and their interactionsin large-scale systems is under the current in-vestigation. To get practical results with betteraccuracy it is important to use longer volumes andlarger times.

3500K X

FIGURE 2 An example of atomic arrangements in crystal-lization processes after simulation time ofa) 300 ps and b) 600 ps.

FIGURE 3 Oxygen and silicon interactions including twoelectron vacancies (Si360). The oxygen atom is located in thecenter.

get exact results. Nevertheless, the proposedsimulation system of crystallization process isuseful to analyze crystal growth rates. To furtherstudy the effects of impurities on a crystal growthand defects formation we show the simulation ofSi cluster interaction with oxygen atoms onFigure 3.

CONCLUSIONS

We have demonstrated the modeling technique ofthe crystallization process of liquid silicon for

Acknowledgments

The authors would like to thank K. Nishihira,M. Ishimaru and T. Motooka from the Depart-ment of Materials Science and Engineering,Kyushu University for their collaboration duringthe course of this work. This research wassponsored by grants from the Fukushima Pre-fectural Foundation for the Advancement ofScience and Education under the project of"Scientific Visualization".

References

[1] Berendsen, H. J. C. and van Gunsteren, W. F., "Moleculardynamics simulations: techniques and approaches", In:Barnes, A. J., Orville-Thomas, W. J. and Yarwood J.(Eds.), "Molecular liquids dynamics and interactions",D. Reidel, Dordrecht, Holland, 1984.

[2] Tersoff, J. (1989). "Modeling solid-state chemistry: Inter-atomic potentials for multicomponent systems", PhysicalReview B, 23(8).

[3] Ishimaru, M., Munetoh, S. and Motooka, T. (1997)."Generation of amorphous silicon structures by rapidquenching: A molecular-dynamics study", Physical ReviewB, 56(23).

[4] "Gaussian 94 Revision E.2", Gaussian, Inc., Pittsburgh,PA, 1995.

[5] Halicioglu, T. (1995). "Comparative study on energy andstructure-related properties for the (100) surface of/3-SIC",Physical Review B, 51(11).

[6] van Gunsteren, W. F. and Berendsen, H. J. C. (1982)."Algorithms for brownian dynamics", Molecular Physics,45(3).

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttp://www.hindawi.com Volume 2010

RoboticsJournal of

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation http://www.hindawi.com

Journal ofEngineeringVolume 2014

Submit your manuscripts athttp://www.hindawi.com

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation http://www.hindawi.com

Volume 2014

The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014

SensorsJournal of


Modelling & Simulation in EngineeringHindawi Publishing Corporation http://www.hindawi.com Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks


Visualization of Large-scale Atomic During the Melting and … · 2019. 8. 1. · VLSIDESIGN 2001,...

Documents

Transcript of Visualization of Large-scale Atomic During the Melting and … · 2019. 8. 1. · VLSIDESIGN 2001,...