  The statistical effects of different conditions in physical vapor deposition,
such as sputter deposition, have on thin film morphology has long been the
subject of interest. One notable effect is that of column development due to
differential chamber pressure in the well-known empirical model called
Thornton's Structure Zone Model. The model is qualitative in nature and
theoretical understanding with quantitative predictions of the morphology is
still lacking due to, in part, the absence of a quantitative description of the
incident flux distribution on the growth front. In this work, we propose an
incident Gaussian flux model developed from a series of binary hard-sphere
collisions and simulate its effects using Monte Carlo methods and a
solid-on-solid growth scheme. We also propose an approximate cosine-power
distribution for faster Monte Carlo sampling. With this model, it is observed
that higher chamber pressures widen the average deposition angle, and similarly
increase the growth of column diameters (or lateral correlation length) and the
column-to-column separation (film surface wavelength). We treat both the column
diameter and the surface wavelength as power laws. It is seen that both the
column diameter exponent and the wavelength exponent are very sensitive to
changes in pressure for low pressures (0.13 Pa to 0.80 Pa); meanwhile both
exponents saturate for higher pressures (0.80 Pa to 6.7 Pa) around a value of
0.6. These predictions will serve as guides to future experiments for
quantitative description of film morphology under a wide range of vapor
pressure.
