The mathematical model for one interface must be specified through one of
ba.SelfAffineFractalModel(...)
ba.LinearGrowthModel(...)
These models define the behavior of autocorrelation function of roughness or, better to say, its Fourier spectrum in the full range of spatial frequencies from 0 to infinity.
ba.SelfAffineFractalModel(sigma, hurst, lateral_corr_length, max_spatial_freq=0.5)
where
sigma
, hurst
, H
with 0<H<1
.
The smaller lateral_corr_length
, max_spatial_freq
, This is the K-correlation model of Palasantzas 1993. The autocorrelation spectrum is
In case there is no cut-off, the real-space roughness correlation
function at the interface is expressed as:
where
The main property is that it remains nearly constant at low
ba.LinearGrowthModel(particle_volume, damp1, damp2, damp3, damp4, max_spatial_freq=0.5)
where
particle_volume
, damp1-damp4
, max_spatial_freq
, This is the model described by Stearns 1993 and extended by Stearns and Gullikson 2000.
The model describes the evolution of the roughness spectrum on the top surface of a growing film. Its autocorrelation spectrum depends not only on the model parameters but also on the film thickness and the spectrum of the underlying interface. Therefore, the model cannot be applied directly to the substrate.
The autocorrelation spectrum is
An essential property of the model is that it describes not only autocorrelation but also cross-correlation properties. Therefore, it does not require cross-correlation to be specified separately.