MD simulations at low dose rates

1. a b Fig.2. Damage level versus temperature at low flux of 3∙107 dpa/s obtained in MD simulations as compared with the analytical model result (a) and with the modified model where an hypothetical defect fraction was included (b). Fig.3. The result of the modified analytical model (with an additional Frenkel pairs fraction) at the flux of 4.9∙1013 ions/cm2s as compared with the experimental data [1]. Dynamic defect annealing in ion implanted SiC; simulation study V.I. Belko and A.Yu. Kuznetsov University of Oslo, Department of Physics, Oslo, Norway Introduction It is known that damage production in ion implanted SiC in the range of 300 – 500 K shows pronounced flux dependence, so called dose rate effect [1]. However this phenomenon is often missing in MD-simulations because (i) the dose rate effect is not so pronounced for the temperatures lower than 200 K and (ii) the addressing requires a time scale unfeasible for MD simulations. Nevertheless, the ion flux together with dose and temperature is a parameter controlling the disordering level in ion implanted samples. • AIMS • to study the defect production phenomena in ion irradiated SiC taking into account the dose rate effect • to specify types of point defects controlling the damage level accumulation in ion irradiated SiC Analytical model: results MD simulations at low dose rates To implement lower dose rates one has to use longer time intervals between primary-knock-on-atom events which in its turn may result in very long simulation time. The dilemma was solved by dynamic changing of the MD box size. Only a part of the initial box was used to describe the system development between the recoil impacts. In details, the displacement cascade initiated with recoil was allowed to evolve for 10 ps such that the collisional and thermal spike stages of the cascade should be asserted. The following system development has homogeneous character in space (defect diffusion and recombination) and one can select certain part of the ensemble as representative. After the development of this selected part for the time to achieve necessary dose rate we fill the space of the initial large box with replica of the small system. Reconstructed system is again allowed to equilibtrate for about 10 ps to repair its unity before the next recoil impact. The results of MD simulations for two MD fluxes, high109 dpa/s and low 3∙107 dpa/s, are presented in Fig.1. We obtained a roughly sigmoid behavior of the disorder level versus temperature, and low flux leads to lower disorder as compared with the high flux in accordance with experimental data [1]. Table II. The probabilities pi fitted using analytical model of amorphization and fitted probabilities , which correspond to the model with additional artificial Frenkel pair type. irradiation irradiation Discussion Based on data summarized in Tables I and II we can assume that dominating interstitial types in MD simulations for the case of light ion irradiation are thetraidral SiTC and split C+Si <100>. In accordance with Table I two annealing stages in Fig.2(a) may correspond to a dissociation of C+Si <100> and SiTC at 250 – 500 K and 900 – 1200 K, respectively. However the agreement in Fig.2(a) between MD simulations data (symbols) and 2-stage annealing model (curve) is not satisfactory in the range of 500 – 700 K. The introduction of any other defect from Table I does not improves the situation since Ea values are either too small or too big to fit the right temperature interval. Interestingly, if we include one extra hypothetical Frenkel pairs fraction with Ea=0.55 andτ0=0.2 in our model and recalculate probabilities for Frenkel pair types (Table II, row 3) the agreement between MD and analytical results improves considerably, see Fig.2(b), called 3-stage annealing model below. This modification partly compensates a weak point of the analytical model: rate equation system do not take into account changing of probabilities for different Frenkel pair types. This fact is also supported with assumption of ref. [4] that migration and annihilation processes on the two sublattices of SiC are coupled. development Fig.1. Damage level obtained in MD simulations versus temperature for two MD ion fluxes. Analytical model Possible stable Frenkel pair configurations were determined in [2] using the MD simulations and proved to obey Arrhenius relationship. The set of interstitial types in stable Frenkel pairs with their barrier energies and pre-exponential factors are presented in the Table I [2]. Table I. Pre-exponential factors and barrier energies of different Frenkel pair types determined in [2]. Comparison with experimental data Applying 3-stage annealing model we may compare our results and experimental data from [1] of SiC irradiation with 100 keV Si+ ions. Assuming defect generation rate of 108 displacements/ion/cm (obtained with SRIM2003) the value (the rate of the Frenkel pairs generation in the unit volume) yields 4.9∙1021 displ/cm3s for the highest experimental flux 4.9∙1013 ions/cm2s [1]. The saturation level for the Frenkel pairs concentration was assumed to be equal 2∙1022 cm-3 [3]. Fig.3 compares the results of the analytical model and experimental data. For normalization purpose the disorder level as found in [1] was multiplied by critical Frenkel pairs concentration 2∙1022 cm-3. Here CTC and CTSi are thetraidral carbon interstitial, surrounding correspondently carbon or silicon atoms, C+C is split carbon interstitial in carbon site, C+Si is split carbon interstitial in silicon site and Si+C vise versa, orientation of the dumbbells being shown. Accounting this stable Frenkel pair types,we applied the analytical model of amorphization to our MD results in the manner close to ref. [3]. Let us assume that the time variation of the number of Frenkel pairs in each fraction is described by the rate equation: Analytical model underestimates the experimental Frenkel pairs concentration possible because it does not account for long-range defect diffusion, clustering and/or amorphous phase formation. This fact is in agreement with the result of so called control experiment in [1]: annealing at 390 K of the sample after the high flux irradiation (for the time of low flux irradiation) does not reduce considerably the damage level, while it influences MD results significantly. where nd is a number of all Frenkel pairs produced by one ion in all MD box, Φ – ion flux (number of ions per MD box per second) , τi is the lifetime for i-fraction of Frenkel pairs and pi is a probability for the metastable Frenkel pair to be of i-type. The resulting damage level is equal to n at time tmax, where D is the fixed dose in our simulations. • Conclusions • MD simulations reveals roughly sigmoid behavior of the disorder level versus temperature, and low flux leads to lower disorder as compared with the high flux in accordance with experimental data [1]. • the model of amorphization accounting only stable Frenkel pairs recombination predicts that thetraidral SiTC and split C+Si<100> are dominating in the MD amorphization-recombination process. • the deviation between analytical and experimental results appears possibly because the model does not account for long-range point defect diffusion, clustering and/or amorphous phase formation. We have considered pi’sas adjustable parameters. Arbitrary selected initial ranges for pi’s were then used for random search of the values providing the best fit to our MD results. The resulting pi’s are presented in the Table II (the 2nd row). Figure 2(a) depicts a number of Frenkel pairs versus temperature at low flux of 3∙107 dpa/s obtained in MD simulations and by means of analytical model. References [1] A.Yu. Kuznetsov, J. Wong-Leung, A. Hallen, C. Jagadish, B.G. Svensson. Journal of Applied Physics 94 (2003) 7112. [2] F. Gao, W.J. Weber. Journal of Applied Physics 94 (2003) 4348. [3] L.Malerba, J.M. Perlado. Journal of Nuclear Materials 289 (2001) 57. [4] Y. Zhang, W.J. Weber, W. Jiang, A. Hallen, G. Possnert. Journal of Applied Physics 91 (2002) 6388