History
The first publication which described the basic features of the KMC method (namely using a cumulative function to select an event and a time scale calculation of the form 1/R) was by Young and Elcock in 1966 (Young 1966). The residence-time algorithm was also published at about the same time in (Cox 1965).
Apparently independent of the work of Young and Elcock, Bortz, Kalos and Lebowitz (Bortz 1975) developed a KMC algorithm for simulating the Ising model, which they called the n-fold way. The basics of their algorithm is the same as that of (Young 1966), but they do provide much greater detail on the method.
The following year Dan Gillespie published what is now known as the Gillespie algorithm to describe chemical reactions (Gillespie 1976). The algorithm is similar and the time advancement scheme essentially the same as in KMC.
There is as of the writing of this (June 2006) no definitive treatise of the theory of KMC, but Fichthorn and Weinberg have discussed the theory for thermodynamic equilibrium KMC simulations in detail in (Fichthorn 1991). A good introduction is given also by Art Voter (Voter 2005), and by A.P.J. Jansen (Jansen 2003),, and a recent review is (Chatterjee 2007) or (Chotia 2008).
In March, 2006 the, probably, first commercial software using Kinetic Monte Carlo to simulate the diffusion and activation/deactivation of dopants in Silicon and Silicon-like materials is released by Synopsys, reported by Martin-Bragado et al. (Martin-Bragado 06).
Read more about this topic: Kinetic Monte Carlo
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