2428 K.NORDLUND AND R.S.AVERBACK 56 cascade temperature evaluated using Eq.(1)]The 600 and 670 K runs resulted in the annihilation of 13 and 11 defects, 5 keV Si 0.1ps respectively. 1.0ps 0 3.0ps In the two cascade events with 50 initial vacancies and 103 ◇ 1n14145 10 ps interstitials,the number of defects after the cascade was …50ps about 25 and 27,which is 15-20 less than in the 0 K events. Inspection of animations of the cascades showed that most of B-8 the defects vanished in the early part of the cascade,in less 102 than 20 ps.Since thermal migration processes account for only around 10 recombinations of defects,there must be an- other defect annealing mechanism active.Since the volume of the liquid region was only about 30%larger at 600 K than 10 at 0 K,it cannot have reached very many more interstitials 0…0008m0 B.080mpma…0-o回6 than in the 0 K runs. 20 40 60 80 100 The liquid region recrystallized much slower than in the 0 Distance from center(A) K runs,parts of the liquid remained even after 20 ps,and its maximum volume was slightly bigger.We know from our earlier work that a fcc interstitial jumps about once every 2 FIG.7.As Fig.5,but for silicon ps at 600 K.3 At the elevated temperatures close to the core of the cascade,the interstitials can be expected to make more increased migration induced by the heating of the cell,which than 10 jumps in 20 ps.Thus,at elevated temperatures inter- are essentially the same mechanisms found by us for low- stitials on the periphery of the melt zone can migrate to it temperature cascades in gold.It appears that these damage before it contracts on resolidification.These interstitials re- annealing mechanisms are significant in several different combine with vacancies in the melt,reducing the number of types of metals. defects. In the event with 50 initial interstitials and no vacancies. 22 of the interstitials got trapped in the liquid and formed a B.Silicon cluster in its center.Since an interstitial has a high formation The silicon results differed dramatically from those in energy in the crystal,but essentially none in a liquid,it is gold.No statistically significant motion of interstitials or va- unlikely that an interstitial which has entered the liquid cancies was observed outside the liquid core of the cascade leaves it again.With no vacancies in the cell,the interstitials (the number of site jumps per defect was less than 0.1).We therefore have to move with the liquid to its center,explain- attribute this to the high migration energies of an interstitial ing the cluster formation. and vacancy in Si.Also,the Si cascade cools down much At lower temperatures the interstitials move much more faster than the Au one (compare Figs.5 and 7).As in gold, slowly and the melt contracts before the interstitials reach it. the heat and pressure waves from the cascade do not appear Since the vacancies are drawn to the center of the cascade,as to have any effect on the defects. we have shown above,interstitials and vacancies become The 5 keV cascade run in an undamaged lattice created 84 well separated:Subsequent motion of the interstitials then interstitials and 90 vacancies.counted using the Wigner- allows them to escape without recombination.Recent work Seitz cell analysis;the structure factor analysis typically by Daulton et al.shows,in fact,that vacancy retention in gave about 10-20%smaller numbers of defects.Some of cascades decreases rapidly with temperatures above about the Wigner-Seitz cells contain more than 2 atoms,explaining 300C.44 The authors say this cannot be explained by disso- why the number of interstitials and vacancies are not equal. lution of the vacancy clusters.We believe the mechanism The number of atoms with a potential energy more than 0.2 found here can explain their result. eV higher than that of undisturbed lattice atoms was found to To conclude the gold results,we have identified three be 910.This agrees well with the results of Diaz de la Rubia damage annealing mechanisms by collision cascades in gold. and Gilmer,who found about 800 final defect atoms with Interstitial and vacancies can recombine during thermal mi- the same criterion in a 5 keV Si cascade using the Stillinger- gration caused by the heating of the crystal by the cascade. Weber potential.5 This indicates that the Tersoff and Defects captured in the liquid formed by the cascade are Stillinger-Weber potentials yield similar results in simula- likely to be forced into the liquid center during the collapse tions of collision cascades. of the liquid,and recombine or (if equal numbers of vacan- The number of defects produced in the runs with initial cies and interstitials are not present in the liquid)form clus- defects are shown in Table I.We see that a 5 keV cascade in ters there.Finally,at increasing temperatures the random silicon creates roughly 100 interstitials and vacancies,re- motion of interstitials makes them increasingly likely to gardless of the initial distribution of point defects in the reach the liquid because of their thermal migration,increas- simulation cell.This is in clear contrast to the results in gold, ing damage annealing. in which the initial and final number of defects were slightly We find similar behavior for other fcc metals,presented in reduced from the initial number.It is evident that the crystal Sec.IIIC below.The a-iron results of Gao et al.-show that regeneration effect present in the collapse of the collision the amount of damage in multiple overlapping cascades satu- cascade in gold is absent in silicon.Furthermore,about 10 of rates.For high-energy cascades they offer two explanations the initial interstitials and vacancies are within the liquid for this:defect loss in the cascade core and defect loss due to zone of the cascade (the total volume of which encompassescascade temperature evaluated using Eq. ~1!# The 600 and 670 K runs resulted in the annihilation of 13 and 11 defects, respectively. In the two cascade events with 50 initial vacancies and interstitials, the number of defects after the cascade was about 25 and 27, which is 15–20 less than in the 0 K events. Inspection of animations of the cascades showed that most of the defects vanished in the early part of the cascade, in less than 20 ps. Since thermal migration processes account for only around 10 recombinations of defects, there must be an￾other defect annealing mechanism active. Since the volume of the liquid region was only about 30% larger at 600 K than at 0 K, it cannot have reached very many more interstitials than in the 0 K runs. The liquid region recrystallized much slower than in the 0 K runs; parts of the liquid remained even after 20 ps, and its maximum volume was slightly bigger. We know from our earlier work that a fcc interstitial jumps about once every 2 ps at 600 K.43 At the elevated temperatures close to the core of the cascade, the interstitials can be expected to make more than 10 jumps in 20 ps. Thus, at elevated temperatures inter￾stitials on the periphery of the melt zone can migrate to it before it contracts on resolidification. These interstitials re￾combine with vacancies in the melt, reducing the number of defects. In the event with 50 initial interstitials and no vacancies, 22 of the interstitials got trapped in the liquid and formed a cluster in its center. Since an interstitial has a high formation energy in the crystal, but essentially none in a liquid, it is unlikely that an interstitial which has entered the liquid leaves it again. With no vacancies in the cell, the interstitials therefore have to move with the liquid to its center, explain￾ing the cluster formation. At lower temperatures the interstitials move much more slowly and the melt contracts before the interstitials reach it. Since the vacancies are drawn to the center of the cascade, as we have shown above, interstitials and vacancies become well separated: Subsequent motion of the interstitials then allows them to escape without recombination. Recent work by Daulton et al. shows, in fact, that vacancy retention in cascades decreases rapidly with temperatures above about 300 °C.44 The authors say this cannot be explained by disso￾lution of the vacancy clusters. We believe the mechanism found here can explain their result. To conclude the gold results, we have identified three damage annealing mechanisms by collision cascades in gold. Interstitial and vacancies can recombine during thermal mi￾gration caused by the heating of the crystal by the cascade. Defects captured in the liquid formed by the cascade are likely to be forced into the liquid center during the collapse of the liquid, and recombine or ~if equal numbers of vacan￾cies and interstitials are not present in the liquid! form clus￾ters there. Finally, at increasing temperatures the random motion of interstitials makes them increasingly likely to reach the liquid because of their thermal migration, increas￾ing damage annealing. We find similar behavior for other fcc metals, presented in Sec. IIIC below. The a-iron results of Gao et al.12 show that the amount of damage in multiple overlapping cascades satu￾rates. For high-energy cascades they offer two explanations for this: defect loss in the cascade core and defect loss due to increased migration induced by the heating of the cell, which are essentially the same mechanisms found by us for low￾temperature cascades in gold. It appears that these damage annealing mechanisms are significant in several different types of metals. B. Silicon The silicon results differed dramatically from those in gold. No statistically significant motion of interstitials or va￾cancies was observed outside the liquid core of the cascade ~the number of site jumps per defect was less than 0.1!. We attribute this to the high migration energies of an interstitial and vacancy in Si. Also, the Si cascade cools down much faster than the Au one ~compare Figs. 5 and 7!. As in gold, the heat and pressure waves from the cascade do not appear to have any effect on the defects. The 5 keV cascade run in an undamaged lattice created 84 interstitials and 90 vacancies, counted using the Wigner￾Seitz cell analysis; the structure factor analysis typically gave about 10–20 % smaller numbers of defects. Some of the Wigner-Seitz cells contain more than 2 atoms, explaining why the number of interstitials and vacancies are not equal. The number of atoms with a potential energy more than 0.2 eV higher than that of undisturbed lattice atoms was found to be 910. This agrees well with the results of Dı´az de la Rubia and Gilmer,5 who found about 800 final defect atoms with the same criterion in a 5 keV Si cascade using the Stillinger￾Weber potential.45 This indicates that the Tersoff and Stillinger-Weber potentials yield similar results in simula￾tions of collision cascades. The number of defects produced in the runs with initial defects are shown in Table I. We see that a 5 keV cascade in silicon creates roughly 100 interstitials and vacancies, re￾gardless of the initial distribution of point defects in the simulation cell. This is in clear contrast to the results in gold, in which the initial and final number of defects were slightly reduced from the initial number. It is evident that the crystal regeneration effect present in the collapse of the collision cascade in gold is absent in silicon. Furthermore, about 10 of the initial interstitials and vacancies are within the liquid zone of the cascade ~the total volume of which encompasses FIG. 7. As Fig. 5, but for silicon. 2428 K. NORDLUND AND R. S. AVERBACK 56