Kinetic Monte Carlo Simulation of Dopant Diffusion in

Kinetic Monte Carlo Simulation of Dopant Diffusion in Crystalline CEC, Inha University Chi-Ok Hwang

Kinetic Monte Carlo (KMC) • MD vs KMC -MD time-spanning problem: automatic time increment adjustment in KMC -KMC (residence-time or n-fold way or Bortz-Kalos. Liebowitz (BKL) ) • KMC conditions (J. Chem. Phys. 95(2), 1090 -1096) - dynamical hierarchy - proper time increments for each successful event - independence of each possible events in system

KMC • Markovian Master Equation: time evolution of probability density : transition probability per unit time : successive states of the system • Detailed balance

Poisson Distribution • Three assumptions of Poisson distribution - 1. - 2. - 3. Events in nonoverlapping time intervals are statistically independent

KMC time increment • KMC time increment

Example • Jump over the barrier due to thermal activation: Boltzmann distribution - ω0: attempt frequency, vibration frequency of the atom (order of 1/100 fs) independent of T in solids • - D: diffusivity - λ: jump distance

Example Start Parameter setting Set the time t =0 Initialize all the rates of all possible transitions in the system Calculate the cumulative function Ri Get a uniform random number Select next event randomly Carry out the event Update configuration & time increment Desired time is reached ? End