Monte Carlo Based Ballistic Deposition Model

The latest version of the Elite module of ATHENA includes a new Monte Carlo based capability for ballistic deposition to model thin film growth by physical vapor deposition. This new ballistic deposition model is useful for modeling metal thinning on trench sidewalls, void and microcrack formations, and local density variations in deposited material layers. The deposition model is based on the ballistic deposition model proposed by Tait et. al. [1]. The model simulates film growth by a random deposition of discs launched with random linear trajectories towards a surface.

The grain-like nature of films deposited onto substrates at low temperatures is modeled, including shadowing and clustering effects that are present in real films, for example, metal deposits made over oxide lines on a silicon substrate. The orientation of the grains in the deposited metal relative to the angle of incidence of the deposition is modeled and voids are predicted (see Figure 1 and Figure 2). Shadowing is predicted for both the 5 and 45 degree cases, in Figures 1 and 2. The columnar structure shows voids present on the left hand side of Figure 1 in accordance with the results of [1].

 

Figure 1. Monte Carlo based ballistic deposition
simulation with the deposit angel set at 5 degrees.

 

Figure 2. Monte Carlo based ballistic deposition
simulation with the deposit angel set at 45 degrees.

 

 

Figures 3 and 4 show deposition into a trench where metal thinning on the trench sidewalls is evident. Figure 3 is simulated without surface diffusion and Figure 4 includes the effect of higher temperature by including surface diffusion. Adding surface diffusion to the simulation in Figure 4 shows an increase in the grain size of the deposited layer.The results of the simulations correspond closely to SEM photos of real structures.

 

Figure 3. Monte Carlo based ballistic deposition
simulation with the deposit angle set at 0 degrees.
Surface diffusion length is 0.0 µm.

 

Figure 4. Monte Carlo based ballistic deposition
simulation with the deposit angle set at 0 degrees.
Surface diffusion length is 0.0 µm.

 

References

[1]. R.N. Tait, T. Smy, and M.J. Brett "A Ballistic Deposition Model for Films Evaporated Over Topography" Thin Solid Films, 187, (1990) 375-384.