### 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.

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66  #!/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): """ Returns 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 """ # Define materials m_vacuum = ba.RefractiveMaterial("Vacuum", 0, 0) m_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 # Define 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(m_si, box_ff) box.rotate(ba.RotationZ(lattice_rotation_angle)) particle_layout = ba.ParticleLayout() particle_layout.addParticle(box) particle_layout.setInterference(interference) # Define sample vacuum_layer = ba.Layer(m_vacuum) vacuum_layer.addLayout(particle_layout) substrate_layer = ba.Layer(m_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, ba.Direction(0.4*deg, 0)) detector = ba.SphericalDetector(200, -0.5*deg, 0.5*deg, 200, 0, 0.6*deg) simulation = ba.ScatteringSimulation(beam, sample, detector) simulation.options().setMonteCarloIntegration(True, 100) return simulation if __name__ == '__main__': bp.parse_args(sim_n=0) sample = get_sample() simulation = get_simulation(sample) result = simulation.simulate() bp.plot_simulation_result(result) 
Examples/scatter2d/RectangularGrating.py

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

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93  #!/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): """ Returns 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 """ # define material mat_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(mat_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(mat_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, ba.Direction(0.4*deg, 0)) n = bp.simargs['n'] 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. """ bp.parse_args(sim_n=200) sample = get_sample() simulation = get_simulation(sample) if not "__no_terminal__" in globals(): simulation.setTerminalProgressMonitor() result = simulation.simulate() if bp.datfile: ba.IOFactory.writeSimulationResult( result, bp.datfile + ".int.gz") field = result.datafield() bp.plot_histogram(field) peaks = ba.FindPeaks(field, 2, "nomarkov", 0.001) xpeaks = [peak[0] for peak in peaks] ypeaks = [peak[1] for peak in peaks] print(peaks) plt.plot(xpeaks, ypeaks, linestyle='None', marker='x', color='white', markersize=10) bp.show_or_export() 
Examples/scatter2d/GratingMC.py