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Interference - Rectangular Grating

This example demonstrates how to perform a simulation of a grating using very long boxes and a 1D lattice. Interference of a 1D lattice may provide useful background information.

Intensity image

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#!/usr/bin/env python3
"""
Simulation of grating using very long boxes and 1D lattice.
Monte-carlo integration is used to get rid of
large-particle form factor oscillations.
"""
import bornagain as ba
from bornagain import ba_plot as bp, deg, micrometer, nm


def get_sample(lattice_rotation_angle=0*deg):
    """
    A sample with a grating on a substrate.
    lattice_rotation_angle = 0 - beam parallel to grating lines
    lattice_rotation_angle = 90*deg - beam perpendicular to grating lines
    """
    # Materials
    vacuum = ba.RefractiveMaterial("Vacuum", 0, 0)
    material_si = ba.RefractiveMaterial("Si", 5.7816e-6, 1.0229e-7)

    box_length, box_width, box_height = 50*micrometer, 70*nm, 50*nm
    lattice_length = 150*nm

    # Particle layout
    interference = ba.Interference1DLattice(
        lattice_length, 90*deg - lattice_rotation_angle)

    pdf = ba.Profile1DGauss(450)
    interference.setDecayFunction(pdf)

    box_ff = ba.LongBoxLorentz(box_length, box_width, box_height)
    box = ba.Particle(material_si, box_ff)
    box.rotate(ba.RotationZ(lattice_rotation_angle))
    particle_layout = ba.ParticleLayout()
    particle_layout.addParticle(box)
    particle_layout.setInterference(interference)

    # Sample
    vacuum_layer = ba.Layer(vacuum)
    vacuum_layer.addLayout(particle_layout)
    substrate_layer = ba.Layer(material_si)

    sigma, hurst, corrLength = 5*nm, 0.5, 10*nm
    roughness = ba.LayerRoughness(sigma, hurst, corrLength)

    sample = ba.MultiLayer()
    sample.addLayer(vacuum_layer)
    sample.addLayerWithTopRoughness(substrate_layer, roughness)
    return sample


def get_simulation(sample):
    beam = ba.Beam(1e8, 0.134*nm, 0.4*deg)
    n = 200
    detector = ba.SphericalDetector(n, -0.5*deg, 0.5*deg, n, 0, 0.6*deg)
    simulation = ba.ScatteringSimulation(beam, sample, detector)
    simulation.options().setMonteCarloIntegration(True, 100)
    return simulation


if __name__ == '__main__':
    sample = get_sample()
    simulation = get_simulation(sample)
    result = simulation.simulate()
    bp.plot_simulation_result(result)
auto/Examples/scatter2d/RectangularGrating.py

To get rid of oscillation arising from large-particle form factors, Monte-carlo integration is used.

Intensity image

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#!/usr/bin/env python3
"""
Simulation of grating using very long boxes and 1D lattice.
Monte-carlo integration is used to get rid of
large-particle form factor oscillations.
"""
import sys
import bornagain as ba
from bornagain import angstrom, ba_plot as bp, deg, micrometer, nm
from matplotlib import pyplot as plt


def get_sample(lattice_rotation_angle=0*deg):
    """
    A sample with a grating on a substrate.
    lattice_rotation_angle = 0 - beam parallel to grating lines
    lattice_rotation_angle = 90*deg - beam perpendicular to grating lines
    """
    # Material
    material_si = ba.RefractiveMaterial("Si", 5.7816e-6, 1.0229e-7)

    box_length, box_width, box_height = 50*micrometer, 70*nm, 50*nm
    lattice_length = 150*nm

    # collection of particles
    interference = ba.Interference1DLattice(
        lattice_length, 90*deg - lattice_rotation_angle)

    pdf = ba.Profile1DGauss(450)
    interference.setDecayFunction(pdf)

    box_ff = ba.LongBoxLorentz(box_length, box_width, box_height)
    box = ba.Particle(material_si, box_ff)
    box.rotate(ba.RotationZ(lattice_rotation_angle))

    particle_layout = ba.ParticleLayout()
    particle_layout.addParticle(box)
    particle_layout.setInterference(interference)

    # assembling the sample
    vacuum_layer = ba.Layer(ba.Vacuum())
    vacuum_layer.addLayout(particle_layout)
    substrate_layer = ba.Layer(material_si)

    sigma, hurst, corrLength = 5*nm, 0.5, 10*nm
    roughness = ba.LayerRoughness(sigma, hurst, corrLength)

    sample = ba.MultiLayer()
    sample.addLayer(vacuum_layer)
    sample.addLayerWithTopRoughness(substrate_layer, roughness)
    return sample


def get_simulation(sample):
    """
    Create and return GISAXS simulation with beam and detector defined
    """
    beam = ba.Beam(1e8, 1.34*angstrom, 0.4*deg)
    n = 200
    det = ba.SphericalDetector(n, -0.5*deg, 0.5*deg, n, 0, 0.6*deg)
    simulation = ba.ScatteringSimulation(beam, sample, det)
    simulation.options().setMonteCarloIntegration(True, 100)
    return simulation


if __name__ == '__main__':
    """
    Runs simulation and returns intensity map.
    """
    sample = get_sample()
    simulation = get_simulation(sample)
    if not "__no_terminal__" in globals():
        simulation.setTerminalProgressMonitor()
    result = simulation.simulate()
    if bp.datfile:
        ba.writeDatafield(result, bp.datfile + ".int.gz")
    peaks = ba.FindPeaks(result, 2, "nomarkov", 0.001)
    xpeaks = [peak[0] for peak in peaks]
    ypeaks = [peak[1] for peak in peaks]
    print(peaks)
    plt.plot(xpeaks,
             ypeaks,
             marker='x',
             linestyle='none',
             color='white',
             markersize=10)

    bp.plot_histogram(result, with_cb=True)

    bp.show_or_export()
auto/Examples/scatter2d/GratingMC.py