Direct simulation Monte Carlo modeling of e-beam metal deposition

Abstract

Three-dimensional direct simulation Monte Carlo ͑DSMC͒ method is applied here to model the electron-beam physical vapor deposition of copper thin films. Various molecular models for copper-copper interactions have been considered and a suitable molecular model has been determined based on comparisons of dimensional mass fluxes obtained from simulations and previous experiments. The variable hard sphere model that is determined for atomic copper vapor can be used in DSMC simulations for design and analysis of vacuum deposition systems, allowing for accurate prediction of growth rates, uniformity, and microstructure.

Molecular Models for DSMC Simulations of Metal Vapor Deposition

“…However, the dimensional mass flux profiles for the various DSMC simulations are significantly different and only the DSMC simulation performed using molecular model 3 agrees well with the experiments. A similar trend was shown for other experimental conditions corresponding to various Kn numbers with model 3 leading to very good agreement between DSMC simulations [5] and the experiments. …”

“…For copper-copper interaction, parameters of Lennard-Jones(LJ) potential based on experimental data on cohesive energy at room temperatures are reported [3] as σ = 2.277 × 10 −10 m and ε = 0.415 eV . The LJ potential parameters obtained using the empirical correlations of Bird et.al [4] are given by [5] σ = 2.242 × 10 −10 m and ε = 0.281 eV . The two LJ potential parameter sets are used to calculate the variation of viscosity as a function of temperature given by [6,7] …”

“…In our DSMC simulations, we have the jet temperature and hence the mass flow rate as a free parameter for reasons described in detail in [5]. The DSMC simulations presented in this work were performed using the 3D version of the SMILE [12] software system and consider six molecular models as tabulated in Table 1.…”

“…The DSMC simulations presented in this work were performed using the 3D version of the SMILE [12] software system and consider six molecular models as tabulated in Table 1. The details of the DSMC simulation parameters used in the simulations are given in [5]. DSMC simulations were performed for various molecular models and jet temperatures.…”

Binary scattering model for Lennard-Jones potential: Transport coefficients and collision integrals for non-equilibrium gas flow simulations

“…While ω for the common gases was taken from Bird, 1 the ω for copper was taken from Venkattraman and Alexeenko. 26 The ω for Al and Au were taken as 1.0 due to lack of data. Typically, the attractive component of the force is important for temperatures corresponding to * ≤ 2.…”