Study of Scaling Exponents of the Surface Evolved in 2 + 1 Dimension through Competitive Growth between Random Deposition and that with Surface Relaxation

Rough surface develops through computer simulation by competition between growth mechanism random deposition (RD) with a probability of occurrence p and growth mechanism random deposition with surface relaxation (RDSR) with a probability of occurrence 1 − p, on L × L square plane for system size L to record the statistical average of time variation of surface roughness W(L, t) and average height H(t) for the model for specific values of L and p. Other than the pure RD model, the entire evolution may be divided into three regions separated by two specific cross-over times t_x and t_sat. The value of interface width at saturation W_sat depends on both L and p. The first growth exponent β₁ increases exponentially with an increase in p and does not depend on L. The values of the second growth exponent β₂, roughness exponent α, dynamic exponent z( = α/β₂ ), and α + z are 0.0234 ± 0.0008, 0.0506 ± 0.0065, 2.1577 ± 0.0073, and 2.2083 ± 0.0138 respectively and they show no dependence on L and p values. Value of the first cross-over time t_x increases exponentially with an increase in p and does not depend on L. Value of the second cross-over time t_sat increases with an increase in both p and L values. The average growth velocity is unity for the model and is independent of both L and p. For the model, the growth velocity is unity and the fractional porosity is zero. The scaling exponents show some deviation from the relevant universality classes and depend on competitive growth probability for this model. No finite-size effect is present in the model.