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Specular reflectivity with interface roughness

This example demonstrates how to compute reflected signal from a multilayered sample with surface roughness. All the experiment layout is exactly the same as the one described in reflectometry tutorial, but now all the layers (except the ambient media) have roughness on the top surface. The roughness is characterized by root-mean-square deviation from the mean surface position $\sigma = 1$ nm.

When comparing the result of the simulation to the result obtained in the reflectometry tutorial, one can notice up to two orders of magnitude attenuation of the reflected signal due to the roughness of the sample.

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#!/usr/bin/env python3
"""
Example of simulating a reflectometry experiment
with a rough sample using BornAgain.

"""
import bornagain as ba
from bornagain import nm, ba_plot as bp, deg, nm


def get_sample():
    # Materials
    vacuum = ba.Vacuum()
    ti_color = (0.05, 0.62, 0.55)
    ti_mat = ba.SLDMaterial("Ti", ti_color, -1.9493e-06, 0)
    ni_color = (0.93, 0.48, 0.14)
    ni_mat = ba.SLDMaterial("Ni", ni_color, 9.4245e-06, 0)
    substrate_color = (0.28, 0.57, 0.82)
    substrate_mat = ba.SLDMaterial("SiSubstrate", substrate_color, 2.0704e-06, 0)

    # roughness
    autocorr = ba.SelfAffineFractalModel(1*nm, 0.7, 25*nm)
    transient = ba.TanhTransient()
    roughness = ba.Roughness(autocorr, transient)

    # Layers
    ambient_layer = ba.Layer(vacuum)
    ti_layer = ba.Layer(ti_mat, 3*nm, roughness)
    ni_layer = ba.Layer(ni_mat, 7*nm, roughness)
    substrate_layer = ba.Layer(substrate_mat, roughness)

    # Periodic stack
    n_repetitions = 10
    stack = ba.LayerStack(n_repetitions)
    stack.addLayer(ti_layer)
    stack.addLayer(ni_layer)
    
    # Sample
    sample = ba.Sample()
    sample.addLayer(ambient_layer)
    sample.addStack(stack)
    sample.addLayer(substrate_layer)

    return sample


def get_simulation(sample):
    n = 500
    scan = ba.AlphaScan(n, 2*deg/n, 2*deg)
    scan.setWavelength(0.154*nm)
    return ba.SpecularSimulation(scan, sample)


if __name__ == '__main__':
    sample = get_sample()
    ba.showSample3D(sample, sample_size=120*nm, seed=0)
    simulation = get_simulation(sample)
    result = simulation.simulate()
    bp.plot_datafield(result)
    bp.plt.show()
auto/Examples/specular/SpecularSimulationWithRoughness.py