Vacancy clustering and diffusion in silicon: Kinetic lattice Monte Carlo simulations

Abstract

Diffusion and clustering of lattice vacancies in silicon as a function of temperature, concentration, and interaction range are investigated by kinetic lattice Monte Carlo simulations. It is found that higher temperatures lead to larger clusters with shorter lifetimes on average, which grow by attracting free vacancies, while clusters at lower temperatures grow by the aggregation of smaller clusters. Long interaction ranges produce enhanced diffusivity and fewer clusters. Greater vacancy concentrations lead to more clusters, with fewer free vacancies, but the size of the clusters is largely independent of concentration. Vacancy diffusivity is shown to obey power law behavior over time, and the exponent of this law is shown to increase with concentration, at fixed temperature, and decrease with temperature, at a fixed concentration.

Kinetic Monte Carlo simulation for the void defects formation in Czochralski silicon growth

“…This result is in good agreement with our experimental results [18]. Compared with the conditions in Haley's research [12], this study focussed on the clustering temperature range and allowed a wider range of vacancy concentration, but the trend agrees well with Haley's research. Figure 2 shows the formation of vacancy clusters for the temperature range.…”

“…Unlike the MD method, the KLMC method can provide valuable mesoscopic information that is difficult to obtain experimentally. Haley [12] shows that vacancy clustering behaviour as a function of temperature, concentration and interaction range is well described using the KLMC method. The diffusivity of the vacancies decreased over time as clusters were formed with the In this work, we describe void defects formation using the KLMC model.…”

Vacancy behavior in Czochralski silicon growth

“…Fig. 4 shows the diffusivity of vacancies as a function of time for variable temperatures such as the work by Haley et al [23]. The vacancy concentration in this case is 2.5 Â 10 18 cm À3 at 720 mm position.…”

“…These values were used as the initial conditions of KLMC model simulations. In the KLMC model, long-range interactions were used to the eighth nearest neighbor, and the system temperature was clustering temperature range (1270-1370 K) [23,24]. The actual simulation volume is 2.0 Â 10 -17 cm 3 and total simulation time is 0.01 s. The formation of vacancy clusters is well described by the KLMC model.…”

Nanovoid nucleation by vacancy aggregation and vacancy-cluster coarsening in high-purity metallic single crystals

“…A widely used methodology to simulate post-MD diffusive processes is kinetic Monte Carlo (KMC). [38][39][40] In KMC, only the discrete jumps of the vacancies are considered, but an a priori knowledge of the transition rates is required. This is not always trivial, as demonstrated by examples found in the literature of complex nonintuitive transitions occurring during surface and bulk diffusion.…”