Improvement of the repulsive part of the classical interatomic potential for SiC

doi:10.1016/S0168-583X(02)01825-6

Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms

Volume 202, April 2003, Pages 18-23

https://doi.org/10.1016/S0168-583X(02)01825-6 Get rights and content

Abstract

In order to enable a better description of ballistic and athermal processes occurring in the initial stage of ion-beam-induced defect formation, the repulsive part of the interatomic potentials of Gao and Tersoff is improved. The first modification concerns the two-body part of the potentials. At small interatomic distances it is replaced by the well-tested potential of Ziegler, Biersack and Littmark (ZBL). For repulsive interactions between zero and some 10 electron volt, an exponential spline function is employed to connect the ZBL potential with the two-body part of the Tersoff and the Gao potential. The modified two-body potentials and their first derivatives are continuous and monotonic over the whole range of repulsive interaction. They are in good agreement with data obtained by density-functional-theory calculations. Furthermore, the three-body part of the Tersoff and the Gao potential is modified in order to avoid the strong dependence of repulsive interactions between two atoms on the bond-order parameter, i.e. on their coordinations. The modification is performed in such a manner that the total potential and its first derivative remain continuous and monotonic for all repulsive interactions.

Introduction

The application of ion implantation for selective electrical doping of SiC as well as the use of SiC in high-radiation environments require the basic physical understanding of radiation-induced defect formation and evolution in this material. Classical molecular dynamics (MD) simulations may be a very successful means to investigate such processes on the atomistic level. However, the reliability of the results obtained by MD calculations depends decisively on the quality of the interatomic potential employed. In investigations of radiation-induced defect production very different properties and processes must be described as accurate as possible: (i) equilibrium properties like lattice parameter and cohesive energy, (ii) defect properties, e.g. formation and migration energies of vacancies and self-interstitials and (iii) dynamic processes during and immediately after atomic collisions. In the present work, the repulsive part of the interatomic potentials of Tersoff [1] and Gao et al. [2] is improved in order to enable a correct treatment of the ballistic and athermal processes occurring in the initial phase of defect formation. For the Tersoff potential, several sets of parameter values are known from the literature. There are at least three parameter sets for the Tersoff function [1], [3], [4] and three sets of cut-off radii [1], [5], [6]. Each parametrization yields sufficiently accurate equilibrium properties of SiC. However, the agreement of the defect energetics determined using the different parameter sets with that obtained by the density functional theory (DFT) [5], [7] is not very good [8]. The values of the parameters for the Tersoff function used in the present work are the same as given in [1] with the following exception: Due to misprints in [1] the value of the parameter d for carbon and the values of the parameters β and h for silicon were taken from [9], [10]. The potential of Gao et al. [2] appears to be a real alternative to the Tersoff potential. For most elementary defects in SiC, it yields a better energetics. However, some deviations still remain between the data obtained by the Gao potential and the results of DFT calculations. In order to enable the modification of the repulsive part of both the Tersoff and the Gao potential by the same mathematical procedure, the Morse-type formulation of the Gao potential was rewritten into the Tersoff form. The modifications described in this paper concern only such parts of the potentials of Tersoff and Gao which are not related to the cut-off radii. Therefore, the cut-off functions are generally omitted in following.

Section snippets

Modifications of the potentials of Tersoff and Gao

At small interatomic distances, the repulsion given by the potentials of Tersoff and Gao is too weak and cannot be used to study energetic atomic collisions. The improvement of the repulsive part of both potentials was performed in the following manner. At first the potential function V was split into a two-body part V⁽²⁾ and a three-body part V⁽³⁾ (V=V⁽²⁾+V⁽³⁾). The two-body part V⁽²⁾(r)=Ae^−λr−Be^−μr (cf. Table 1) was replaced by the relation $U^{(2)} (r)= V_{ZBL} (r)+ Δ V_{ZBL}, 0<r<r_{l}, A^{′} e^{−λ^{′}r} −B^{′} e^{−μ^{′}r}, r_{l} ⩽r⩽r_{h}, V$

Conclusions

The repulsive part of the interatomic potentials of Gao and Tersoff was improved. The modified potentials allow a more realistic treatment of energetic atomic collisions in the framework of classical MD simulations of ion-beam-induced defect formation in SiC. Since such ballistic processes initiate the defect production, the quality of the interatomic potential employed does also influence the accuracy of the final results of MD calculations, like the type and the amount of defects formed.

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¹: Present address: Arizona State University, Department of Chemical and Materials Engineering, Tempe, AZ, USA.

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Improvement of the repulsive part of the classical interatomic potential for SiC

Abstract

Introduction

Section snippets

Modifications of the potentials of Tersoff and Gao

Conclusions

Nucl. Instr. and Meth. B

J. Nucl. Mater.

Nucl. Instr. and Meth. B

Phys. Rev. B

Modell. Simul. Mater. Sci. Eng.

Phys. Rev. B

Phys. Rev. B