“…46,47 The surface roughness ω ( l , t ) usually exhibits the dynamic scaling relation ω ( l , t ) = t β f ( u ≡ l / ξ ( t )) in space and time with the following scaling function: 67
Thus,
Here, the lateral correlation length ξ ( t ) ∼ t 1/ z , where z is the dynamic exponent, α is the roughness exponent, β is the growth exponent, and the time exponent κ ≡ β − α / z = 0 and >0 correspond to normal and anomalous roughening, respectively. 15,18,48,67 ω ( l , t ) exhibits Family–Vicsek dynamic scaling, 18 i.e. , normal roughening, in discrete growth modes for particle deposition 15,18 and growth fronts described by EW 20 or KPZ 21 continuum dynamic growth equations.…”