Accelerated atomistic simulation study on the stability and mobility of carbon tri-interstitial cluster in cubic SiC
Introduction
Silicon carbide is a wide-band-gap semiconductor material considered for high-power, high-frequency and high-temperature applications [1], [2]. In its cubic form, SiC has been also proposed as a candidate structural material for next generation nuclear reactors due to the outstanding mechanical properties, good thermal stability and low neutron capture cross section of this material [3], [4], [5]. Stable defect clusters are known to form in SiC during ion implantation both in semiconductor applications [6] and in nuclear radiation environments [7], [8]. These clusters have important consequences both for electronic properties and for radiation resistance of SiC [6], [7], [8].
Many efforts have been reported on the structure of stable defect clusters. For instance, Mattausch et al. [9], [10], [11] studied the Local Vibrational Modes (LVMs) of a series of carbon clusters consisting of a few interstitials and antisites, and proposed new candidates for the so-called P–U, P–T and DII photoluminescence centers; Jiang et al. [12], [13] proposed a new ground state (GS) as well as a few low energy states of small carbon interstitial clusters with sizes up to 6 interstitials in cubic SiC. Bockstedte et al. [10] investigated the annealing hierarchy of defects based on formation and binding energies of small defect clusters that had been reported in the literature. Defects clusters were assumed to act as aggregation centers of point defects in a low temperature regime (T < 1000 °C) and act as re-emitting sources of point defects by dissociation in a high temperature regime (T > 1000 °C). Up to this point, the mobility and dynamics of the defect clusters in SiC has not been investigated. Quantification of cluster dynamics is, however, important for understanding of processes that control high-temperature annealing of defects introduced during ion implantation and for predicting radiation resistance of SiC under given temperature and irradiation conditions. In addition to migration and dissociation of the clusters, cluster rotation is also of potential interest. For instance, recent studies of irradiation creep of SiC [14], [15] suggested that anisotropic distribution of small dislocation loops on {1 1 1} planes under the applied stress is responsible for the experimentally observed irradiation creep and swelling. These loops were hypothesized to be formed by self-interstitial clusters, and their formation and rotation behavior under stress is responsible for the anisotropic distribution. The authors characterized distribution of interstitial loops with sizes on the order of nanometers. It was found that while distribution of these loops was isotropic in the absence of stress, under tensile stress that distribution changed to anisotropic with about 20% more loops lying in planes perpendicular to the stress axis. The authors demonstrated that large (tens of nanometers sized) loops are not sufficient to explain the observed swelling and creep, and therefore the small (few nanometer and smaller sized) loops need to be accounted when trying to explain the aforementioned irradiation phenomena.
A major challenge in predicting dynamics of defect clusters in SiC lies in the high defect migration barriers in this material and in short simulation time scales of standard molecular dynamics (MD) simulations. Multiple accelerated techniques have been developed in the community to extend MD time scale limitations, such as hyperdynamics, parallel replica dynamics and temperature-accelerated dynamics developed by Voter [16], [17], [18]. Another widely used technique for long-time scale simulation is kinetic Monte Carlo (kMC). In this technique, the system hops from one energy minimum to another based on the known transition probabilities. The time is advanced in each hop based on the transition state theory. However, kMC requires a predefined event lists for transitions out of each minimum, which is very challenging to achieve for cluster migration due to the unknown transitions and numerous intermediate states involved in cluster dynamics. To address this problem, several open-ended saddle point search algorithms have been proposed, including the activation–relaxation technique (ART) [19], [20], [21], [22], [23], the dimer method [24], and the autonomous basin climbing method [25]. When the kMC is combined with one of these algorithms, an on-the-fly kMC scheme can be developed and it can work on systems with complicated energy surface for a long-time scale simulation.
In this paper, we employ the kinetic activation–relaxation (k-ART) technique to investigate dynamics of C interstitial clusters in SiC. Specifically, we focus on migration and rotation of the (CBC)3 cluster, which has been proposed to be one of the most stable small interstitial clusters in irradiated SiC [13]. This cluster is composed of three carbon interstitials occupying 3 neighboring C–Si bond center sites in the {1 1 1} plane and it is a common building block of other small carbon interstitial clusters [13]. For example, the GS of carbon penta-interstitial cluster is composed of a (CBC)3 cluster with a neighboring (CBC)2 complex, and the GS of carbon hexa-interstitial cluster is composed of two neighboring (CBC)3 clusters. The kinetic activation–relaxation technique (k-ART) based simulation protocol developed here for studies of the (CBC)3 cluster can be later employed to study other defects in this material.
Section snippets
k-ART sampling
The rotation and migration paths of the (CBC)3 cluster are investigated using ART, a single-ended eigenvector-following method developed by Barkema and Mousseau [19] and modified later by several groups [26], [27], [28]. In the activation phase, the system is pushed out of equilibrium by displacing selected atoms in steps of length 0.1 Å in random directions of the configuration space and a limited energy minimization is applied in the orthogonal hyperplane after each step. Selected atoms can be
Results
The two most stable configurations of the (CBC)3 cluster in the cubic SiC are shown in Fig. 1 and one can see that these clusters lie within the {1 1 1} planes. A C-centered (or Si-centered) cell refers to the cell where the lattice atom right above the center of the (CBC)3 cluster is C (or Si). The C- and Si-centered cells are shown in Fig. 1(a) and (b), respectively. Jiang et al. [12] showed that the (CBC)3 cluster within a C-centered cell is the GS of carbon tri-interstitial clusters in cubic
Conclusions
Using a combination of k-ART sampling with EDIP and ab initio based CI-NEB calculations, we have determined the migration and dissociation energies of the (CBC)3 cluster in cubic SiC, which is the most stable small C interstitial clusters in SiC among the known clusters in SiC. The fastest migration path has the energy barrier of 4.29 eV and the second fastest path has a comparable barrier of 4.37 eV. The dissociation barrier of the (CBC)3 cluster into a non-interacting (CBC)2 defect and Csp<100>
Acknowledgements
This research is supported by the U.S. Department of Energy, Office of Basic Energy Sciences Grant No. DE-FG02-08ER46493. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant Number OCI-1053575.
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