### 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 67 68 69  #!/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 numpy, sys import bornagain as ba from bornagain import deg, micrometer, nm, nm2, kvector_t def get_sample(lattice_rotation_angle=0.0*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 """ # defining materials m_vacuum = ba.HomogeneousMaterial("Vacuum", 0.0, 0.0) m_si = ba.HomogeneousMaterial("Si", 5.78164736e-6, 1.02294578e-7) box_length, box_width, box_height = 50*micrometer, 70*nm, 50*nm lattice_length = 150*nm # collection of particles interference = ba.InterferenceFunction1DLattice( lattice_length, 90.0*deg - lattice_rotation_angle) pdf = ba.FTDecayFunction1DGauss(450.0) interference.setDecayFunction(pdf) box_ff = ba.FormFactorLongBoxLorentz(box_length, box_width, box_height) box = ba.Particle(m_si, 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 vacuum_layer = ba.Layer(m_vacuum) vacuum_layer.addLayout(particle_layout) substrate_layer = ba.Layer(m_si) roughness = ba.LayerRoughness() roughness.setSigma(5.0*nm) roughness.setHurstParameter(0.5) roughness.setLatteralCorrLength(10.0*nm) multi_layer = ba.MultiLayer() multi_layer.addLayer(vacuum_layer) multi_layer.addLayerWithTopRoughness(substrate_layer, roughness) return multi_layer def get_simulation(sample): beam = ba.Beam(100000000.0, 0.134*nm, ba.Direction(0.4*deg, 0*deg)) detector = ba.SphericalDetector(200, -0.5*deg, 0.5*deg, 200, 0*deg, 0.6*deg) simulation = ba.GISASSimulation(beam, sample, detector) simulation.getOptions().setMonteCarloIntegration(True, 100) return simulation if __name__ == '__main__': import ba_plot sample = get_sample() simulation = get_simulation(sample) ba_plot.run_and_plot(simulation) 
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 94 95 96 97 98 99 100  #!/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 deg, angstrom, nm, micrometer import ba_plot from matplotlib import pyplot as plt def get_sample(lattice_rotation_angle=0.0*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 """ # defining materials m_vacuum = ba.HomogeneousMaterial("Vacuum", 0.0, 0.0) m_si = ba.HomogeneousMaterial("Si", 5.78164736e-6, 1.02294578e-7) box_length, box_width, box_height = 50*micrometer, 70*nm, 50*nm lattice_length = 150*nm # collection of particles interference = ba.InterferenceFunction1DLattice( lattice_length, 90.0*deg - lattice_rotation_angle) pdf = ba.FTDecayFunction1DGauss(450.0) interference.setDecayFunction(pdf) box_ff = ba.FormFactorLongBoxLorentz(box_length, box_width, box_height) box = ba.Particle(m_si, 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 vacuum_layer = ba.Layer(m_vacuum) vacuum_layer.addLayout(particle_layout) substrate_layer = ba.Layer(m_si) roughness = ba.LayerRoughness() roughness.setSigma(5.0*nm) roughness.setHurstParameter(0.5) roughness.setLatteralCorrLength(10.0*nm) multi_layer = ba.MultiLayer() multi_layer.addLayer(vacuum_layer) multi_layer.addLayerWithTopRoughness(substrate_layer, roughness) return multi_layer 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, 0.0*deg)) det = ba.SphericalDetector(200, -0.5*deg, 0.5*deg, 200, 0*deg, 0.6*deg) simulation = ba.GISASSimulation(beam, sample, det) simulation.getOptions().setMonteCarloIntegration(True, 100) return simulation def run_simulation(): """ Runs simulation and returns intensity map. """ sample = get_sample() simulation = get_simulation(sample) if not "__no_terminal__" in globals(): simulation.setTerminalProgressMonitor() simulation.runSimulation() return simulation.result() def simulate_and_plot(): interactive = True result = run_simulation().histogram2d() ba_plot.plot_histogram(result) 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, linestyle='None', marker='x', color='white', markersize=10) plt.show() if __name__ == '__main__': simulate_and_plot() 
GratingMC.py