Kinetic Monte Carlo simulations for transient thermal fields: Computational methodology and application to the submicrosecond laser processes in implanted silicon

Pulsed laser irradiation of damaged solids promotes ultrafast nonequilibrium kinetics, on the submicrosecond scale, leading to microscopic modifications of the material state. Reliable theoretical predictions of this evolution can be achieved only by simulating particle interactions in the presence of large and transient gradients of the thermal field. We propose a kinetic Monte Carlo (KMC) method for the simulation of damaged systems in the extremely far-from-equilibrium conditions caused by the laser irradiation. The reference systems are nonideal crystals containing point defect excesses, an order of magnitude larger than the equilibrium density, due to a preirradiation ion implantation process. The thermal and, eventual, melting problem is solved within the phase-field methodology, and the numerical solutions for the space- and time-dependent thermal field were then dynamically coupled to the KMC code. The formalism, implementation, and related tests of our computational code are discussed in detail. As an application example we analyze the evolution of the defect system caused by P ion implantation in Si under nanosecond pulsed irradiation. The simulation results suggest a significant annihilation of the implantation damage which can be well controlled by the laser fluence.

Figure 1

Schema of no-lattice kinetic Monte Carlo environment which considers interstitial (dark balls) and vacancy (white balls) defects in mobile (surrounded by arrows) or clustered configuration. The two panels refer to the melting front evolution induced by a laser irradiation process. Particle annhilation in the molten region [red (dark gray)] and defect ripening process in solid phase [yellow (light gray)] are also represented.

Figure 2

Total interstitial (dashed) and vacancy (dotted) defect density: dark lines refer to the as-implanted defects obtained by SRIM simulation; green (light gray) and red (dark gray) lines refer, respectively, to the residual defect density after room temperature evolution obtained from the atomistic KMC simulation and from the continuous PDE model. The inset shows the difference between total $I$- and $V$-type defects as obtained after SRIM simulation.

Figure 3

Time evolution of the temperature at three different positions for the 2.6 J/cm${}^2$ laser process: solid, dashed, and dotted lines refer, respectively, to the thermal field at 0.0, 0.5, and 1.0 μm below the irradiated surface (0.0 μm). The inset shows the evolution of the temperature variation between the points 0.0 and 1.0 μm.

Figure 4

Time evolution of the melt depth during the melting laser processes with 2.6 (dotted), 3.0 (dashed), and 3.6 (solid) J/cm${}^2$ laser fluences.

Figure 5

Postanneal total interstitial (filled symbols) and vacancy (empty symbols) defect densities for 2.6 [red (dark gray)] and 3.0 [green (light gray)] J/cm${}^2$ laser fluences. Dark squares refer to the simulated total interstitial and vacancy defects after KMC room temperature evolution. Dashed ($I$) and dotted ($V$) lines refer to the continuous simulation carried out by means of the Giles et al. (upper panel) and Rafferty et al. (lower panel) parameters for cluster dissolution rates.

Figure 6

Interstitial concentrations after room temperature (empty squares) and one-pulse (filled squares) laser irradiation of 2.6 J/cm${}^2$ laser fluence obtained by means of the KMC code. Dashed lines refer to PDE simulation for the same process carried out with the Giles et al. (upper panel) and Rafferty et al. (lower panel) parameters for the cluster dissolution rates. Dark, red (dark gray), and green (light gray) lines refer, respectively, to distributions of clusters formed by two, three, and four defects.

Figure 7

Vacancy concentrations after room temperature (empty squares) and one-pulse (filled squares) laser irradiation of 2.6 J/cm${}^2$ laser fluence obtained by means of the KMC code. Dotted lines refer to PDE simulation for the same process carried out with the Giles et al. (upper panel) and Rafferty et al. (lower panel) parameters for the cluster dissolution rates. Dark, red (dark gray), and green (light gray) lines refer, respectively, to distributions of clusters formed by two, three, and four defects.

Figure 8

Interstitial concentrations after room temperature (empty squares) and one-pulse (filled squares) laser irradiation of 3.0 J/cm${}^2$ laser fluence obtained by means of the KMC code. Dashed lines refer to PDE simulation for the same process carried out with the Giles et al. (upper panel) and Rafferty et al. (lower panel) parameters for the cluster dissolution rates. Dark, red (dark gray), and green (light gray) lines refer, respectively, to distributions of clusters formed by two, three, and four defects.

Figure 9

Vacancy concentrations after room temperature (empty squares) and one-pulse (filled squares) laser irradiation of 3.0 J/cm${}^2$ laser fluence obtained by means of the KMC code. Dotted lines refer to PDE simulation for the same process carried out with the Giles et al. (upper panel) and Rafferty et al. (lower panel) parameters for the cluster dissolution rates. Dark, red (dark gray), and green (light gray) lines refer, respectively, to distributions of clusters formed by two, three, and four defects.