### Interference - Rectangular Grating

This example demonstrates how to perform a simulation of a grating using very long boxes and a 1D lattice. To get rid of oscillation arising from large-particle form factors, Monte-carlo integration is used.

Interference of a 1D lattice may provide useful background for this example.

  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  """ 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 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_ambience = ba.HomogeneousMaterial("Air", 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.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 air_layer = ba.Layer(m_ambience) air_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(air_layer) multi_layer.addLayerWithTopRoughness(substrate_layer, roughness) return multi_layer def get_simulation(): """ Create and return GISAXS simulation with beam and detector defined """ simulation = ba.GISASSimulation() simulation.setDetectorParameters(200, -0.5*deg, 0.5*deg, 200, 0.0*deg, 0.6*deg) simulation.setBeamParameters(1.34*angstrom, 0.4*deg, 0.0*deg) simulation.setBeamIntensity(1e+08) 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, cmap='jet', aspect='auto') 
RectangularGrating.py