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Kinetic Monte Carlo Simulation of Dopant Diffusion in Crystalline

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) )

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Kinetic Monte Carlo Simulation of Dopant Diffusion in Crystalline

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

  2. 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

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

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

  5. KMC time increment 평균적 발생 확률 t 시간 동안 ne번의 사건이 발생할 확률

  6. KMC time increment • KMC time increment

  7. 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

  8. 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 Start End Select next event randomly Carry out the event Update configuration & time increment Desired time is reached ? Example

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