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), ) - 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 Events in nonoverlapping time intervals are statistically independent

KMC time increment 평균적 발생 확률 t 시간 동안 n e 번의 사건이 발생할 확률

KMC time increment

Example Jump over the barrier due to thermal activation: Boltzmann distribution - ω 0 : attempt frequency, vibration frequency of the atom (order of 1/100 fs) independent of T in solids - D: diffusivity - λ: jump distance

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