New Phonon Dynamics in a Diamond Crystal during Post-Annealing

Abstract

<p>A new mesoscopic response in a crystal during post-annealing (PA) after ion implantation has been discovered. PA is an indispensable procedure for activating the implanted dopant center by retrieving the lost crystallinity of the host crystal, which usually elapses over periods longer than a few milliseconds. By using an empirical molecular-dynamics simulation, we examined what actually happened during extended PA for up to one nanosecond in case of sub-keV N₂ beam implantation into bulk diamond at room temperature with annealing at 1000 K. While observing the changes in the long-range-order (LRO) parameter, a notable phase transition from the crystalline to the amorphous state (CA transition) occurred synergistically at approximately a few picoseconds (ps). After the CA transition, PA was initiated. A few tens of ps later, a sequence of restoration spikes was observed in LRO parameter with a regular time interval of 70–80 ps. Each sharp peak showed the spontaneous restoration of “amorphous -> crystal -> amorphous” transitions. This process may trigger a “<em>critical state”</em> that occurs during the slow and steady recovery of the lost crystallinity in the early stages of PA. It was found that annealing not only enhances the vibration amplitude of the individual atoms in the bulk but also causes <em>phonon-assisted restoration</em> in a mesoscopic space.</p

The Phase Transition during Post Annealing

“…The lower the T A , the shorter the regular time interval (δt) between spikes increased, e.g., 120 ps (E 0 = 200 eV/atom and T A = 300 K), 100 ps at 500 K (Fig. 1a), and δt = 70-80 ps at 1,000K [20]. Such a cooperative profile implies the presence of phonon-like movement of target atoms.…”

“…For this sake, the degree of restoration is monitored during PA procedure via the time series of the LRO parameter [18][19][20], which we call the LRO pattern for brevity. Values of "LRO = 1" and "LRO = 0" indicate a perfect crystalline state and an amorphous one, respectively.…”

“…If it is segmented parallel to the surface, it yields LRO(z). If it is segmented finer by further slicing those cylinders vertically parallel to the surface, it yields LRO(r, z) [20]. In this article, we evaluated LRO(r) for the surface region at z (nm) < 1.0, because the depth(z)-dependence of LRO of a diamond subjected by sub-keV N 2 beam was very weak and looked ignorable [3] .…”