Interference 1D lattice

In this example we simulate the scattering from infinite 1D repetition of rectangular patches (rectangular grating). This is done by using the interference function of a 1D lattice together with very long boxes.

  • By-default, the axis of the one-dimensional lattice coincides with the $x$-axis of the reference cartesian frame, so it coinsides with the beam direction.
  • Long boxes are placed along a one-dimensional lattice on top of substrate, the lattice_length parameter corresponds to the grating period.
  • The size of boxes is initially chosen to form a grating which is perpendicular to the beam (long side of the box is along $y$-axis).
  • Please keep in mind, that length, width, height in the FormFactorBox(length, width, height) constructor correspond to the directions in the $x,y,z$ axes, in that order, so to achieve the desired setup we use the values: length= $10$ nm, width= $10000$ nm, height= $10$ nm.
  • The whole grating is rotated at the end by an angle of $45^{\circ}$ with respect to the beam axis. This is achieved by rotating both the 1D lattice and the long boxes (see lines 25 and 34).
  • To avoid the problem of rapidly oscillating form factors of long boxes (see this example for more details), the simulation is performed in monte carlo integration mode.

Real-space model

Sketch

Intensity image

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"""
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 deg, angstrom, nm


def get_sample(lattice_rotation_angle=45*deg):
    """
    Returns a sample with a grating on a substrate,
    modelled by very long boxes forming a 1D lattice with Cauchy correlations.
    """
    # defining materials
    m_ambience = ba.HomogeneousMaterial("Air", 0.0, 0.0)
    m_substrate = ba.HomogeneousMaterial("Substrate", 6e-6, 2e-8)
    m_particle = ba.HomogeneousMaterial("Particle", 6e-4, 2e-8)

    box_length, box_width, box_height = 10*nm, 10000*nm, 10*nm
    lattice_length = 30*nm

    # collection of particles
    interference = ba.InterferenceFunction1DLattice(
        lattice_length, lattice_rotation_angle)
    pdf = ba.FTDecayFunction1DCauchy(1000.0)
    interference.setDecayFunction(pdf)

    box_ff = ba.FormFactorBox(box_length, box_width, box_height)
    box = ba.Particle(m_particle, box_ff)

    particle_layout = ba.ParticleLayout()
    particle_layout.addParticle(
        box, 1.0, ba.kvector_t(0.0, 0.0, 0.0), ba.RotationZ(lattice_rotation_angle))
    particle_layout.setInterferenceFunction(interference)

    # assembling the sample
    air_layer = ba.Layer(m_ambience)
    air_layer.addLayout(particle_layout)
    substrate_layer = ba.Layer(m_substrate)

    multi_layer = ba.MultiLayer()
    multi_layer.addLayer(air_layer)
    multi_layer.addLayer(substrate_layer)
    return multi_layer


def get_simulation():
    """
    Create and return GISAXS simulation with beam and detector defined
    """
    simulation = ba.GISASSimulation()
    simulation.setDetectorParameters(200, -1.0*deg, 1.0*deg,
                                     200, 0.0*deg, 2.0*deg)
    simulation.setBeamParameters(1.0*angstrom, 0.2*deg, 0.0*deg)
    simulation.getOptions().setMonteCarloIntegration(True, 100)
    return simulation


def run_simulation():
    """
    Runs simulation and returns intensity map.
    """
    simulation = get_simulation()
    simulation.setSample(get_sample())
    simulation.setTerminalProgressMonitor()
    simulation.runSimulation()
    return simulation.result()


if __name__ == '__main__':
    result = run_simulation()
    ba.plot_simulation_result(result, intensity_min=1e-03, cmap='jet', aspect='auto')
Interference1DLattice.py