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

Abstract

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.

Kinetic Monte Carlo simulations of boron activation in implanted Si under laser thermal annealing

“…Hence, it is mandatory to couple the stochastic method with a phase-field model that properly simulates the rapidly varying non-uniform thermal and phase (if melting occurs) fields. 9) The current version includes dopant atoms that can reside in a substitutional position B s or form a complex with interstitial defects, i.e., BICs. 10) Without loss of generality, we assumed that I and V point defects as well as the BI complex (one dopant atom bound to one I point defect) are the only mobile species, and that defect clusters X m (X = I or V) as well as the dopant-defect cluster B n I m (a cluster formed by n dopant atoms and m interstitials) can only absorb or emit mobile defects.…”

“…The periodic and boundary conditions were set as in Ref. 9. Considering the values of R melt and R p , the choice of a simulation box (X b © Y b © Z b ) with a depth of Z b = 600 nm (in the direction of laser irradiation) reliably approximates a bulk sample.…”

Dopant dynamics and defects evolution in implanted silicon under laser irradiations: A coupled continuum and kinetic Monte Carlo approach

“…[11]. The projected range of the boron ions (30 keV) is 120 nm and the maximum melt depth corresponding to the highest laser fluence employed (2.6 cm -2 ) is 140 nm, so the choice of a simulation box ( × × ) with a depth of = 600 nm (in the direction of laser laser irradiation) ensures the validity of the real bulk approximation.…”

“…The implementation details for the pure defect system can be found in Ref. [11]. Dopant atoms can reside in a substitutional position or form a complex with interstitial defects, i.e.…”

“…KMC parameters (i.e. exponential prefactors, migration and binding energies) have been taken from literature [11]- [13].…”