sas3d_example1 - Jupyter Notebook

Menu Python 3 Trusted File Edit View Insert Cell Kernel WidgetsHelp In [2]: import numpy as npimport escape as escfrom escape.utils import show. . .3D structures, potential object and small angle scattering (experimental)¶ In this notebook we describe two other entites for sample description: potential and geometry, which are used for creation of structured layered samples. Morphology analysis and metrology of structured samples is of great interest nowadays for electronics industry as well as for scinetific applications. The potential module is under development at the moment and some features are still buggy and do not function properly. Please do not use it for real applications. We start with a simple example of rectangular gratings periodically aligned on a substrate. This kind of gratings can be prepared with ion etching technique, for example. First we should define parameters for the structure unit, a single grating. In [3]: wx=esc.par("Width X", 50, units="nm")wy=esc.par("Width Y", 500, units="nm")wz=esc.par("Width Z", 50, units="nm"). . .Potential is not a functor object, but internally performs calculations and, thus, requires variables (𝑄𝑥Qx, 𝑄𝑦Qy, 𝑄𝑧Qz). In [4]: qx=esc.var("Qx")qy=esc.var("Qy")qz=esc.var("Qz"). . .Since potential formula in scattering theory depends on scattering length density, the potential object requires material as input parameter. Next we create material. In [5]: #we set sldre = 4e-6 1/A^2 and sldim = 0mat1=esc.amorphous("", 4e-6, 0, color="#FFFF00"). . .We can create now a potential object for a grating located at position (0, 0, wz/2) In [6]: V=esc.box("", qx, qy, qz, mat1, wx, wy, wz, pos=[ (0.0, 0.0, wz/2) ])show(V, title="Box Grating")Box GratingWidth X[nm]:50.00Width Y[nm]:500.0Width Z[nm]:50.00 INFO: Refreshed picking FBO to size (337, 168)INFO: Found 0 X3D and nodes...INFO: X3DOM 1.8.2-dev, Build: 7180, Revison: , Date: Tue Jul 21 09:40:22 2020 -0400INFO: Time for setup and init of GL element no. 0: 196 ms.INFO: activate FogBindable null/defaultX3DFogNodeINFO: register FogBindable null/defaultX3DFogNodeINFO: create new Fog for X3DFogNode-stackINFO: activate ViewpointBindable null/Oblique viewINFO: activate first X3DViewpointNode for X3DViewpointNode-stackINFO: activate BackgroundBindable null/INFO: activate first X3DBackgroundNode for X3DBackgroundNode-stackINFO: System ready.INFO: activate NavigationInfoBindable null/INFO: activate first X3DNavigationInfoNode for X3DNavigationInfoNode-stackINFO: activate EnvironmentBindable null/defaultX3DEnvironmentNodeINFO: register EnvironmentBindable null/defaultX3DEnvironmentNodeINFO: create new Environment for X3DEnvironmentNode-stackWARNING: Fallback to inefficient multi-index mode since creaseAngle=0.INFO: register ViewpointBindable null/Oblique viewINFO: register NavigationInfoBindable null/INFO: NavType: undefinedINFO: Switch to examine mode.INFO: register BackgroundBindable null/INFO: webgl2 context found Vendor: Mozilla Google Inc., Renderer: Mozilla ANGLE (Intel(R) UHD Graphics 620 Direct3D11 vs_5_0 ps_5_0), Version: WebGL 2.0, ShadingLangV.: WebGL GLSL ES 3.00, MSAA samples: 4 Extensions: EXT_color_buffer_float, EXT_float_blend, EXT_texture_compression_bptc, EXT_texture_filter_anisotropic, OES_texture_float_linear, OVR_multiview2, WEBGL_compressed_texture_s3tc, WEBGL_compressed_texture_s3tc_srgb, WEBGL_debug_renderer_info, WEBGL_debug_shaders, WEBGL_lose_contextINFO: Initializing X3DCanvas for [x3dom-1595347004033-canvas]INFO: Creating canvas for (X)3D element...INFO: Found 1 X3D and nodes...INFO: X3DOM 1.8.2-dev, Build: 7180, Revison: , Date: Tue Jul 21 09:40:22 2020 -04000 . . .. . .Calculating Small Angle Scattering intensity.¶ For the calculation of small angle scattering intensity map, we should create a grid of coordinates (𝑄𝑥Qx, 𝑄𝑦Qy, 𝑄𝑧Qz) first. In [7]: #Wavelength Cu-Kalphawl = 1.5405 #Size of a gridsz = 512#magnitude of the wave vectork0 = 2.0 * np.pi / 1.5405#angle arrays for the calculation of scttering vector componentsa = np.linspace(-3, 3, sz)b = np.linspace(-3, 3, sz)#scattering vector meshgridav, bv = np.meshgrid(a, b)#caluclating scattering vector component for every point_qy = k0 * np.sin(bv * np.pi / 180.0)_qx = k0 * np.cos(bv * np.pi / 180.0)*np.sin(av * np.pi / 180.0)_qz = k0 * np.cos(bv * np.pi / 180.0)*np.cos(av * np.pi / 180.0)-k0#creating coordinates array of type (x0, y0, z0, x1, y1, z1, ...)c=np.column_stack((_qx.flatten(), _qy.flatten(), _qz.flatten())).flatten(). . .We have demonstrated how to define a potential for a single grating. The gratings, however, are periodically aligned along one of the axis, let it be 𝑋X - axis, forming a lattice. This lattice is a function of one variable and can be created as following In [8]: #this lattice has a limited size of 10 gratingsT=esc.par("Period X", 100, units="nm")latx = esc.lattice("", qx, T, 10)show(latx, coordinates=np.linspace(-0.2, 0.2, sz))Period X[nm]:100.0Figure . . .We create Small Angle Cross section kernel as following In [9]: I = esc.sas("", qx, qy, qz, V, latx, multithread=True)show(I, coordinates=c, cblog=True, cbmin=1, rows=sz, plot_type="map", xlabel="Qx", ylabel="Qy")Width X[nm]:50.00Width Y[nm]:500.0Width Z[nm]:50.00Period X[nm]:100.0Figure . . .2D lattice¶ What if our shapes form a 2d cubic lattice on a substrate surface. Below we demonstrate how to define 2d lattice by means of multiplication of two lattice functors. For convinience we create a new box potential with reduced width in 𝑌Y - direction. In [10]: wy=esc.par("Width Y", 50, units="nm")V=esc.box("", qx, qy, qz, mat1, wx, wy, wz, pos=[ (0.0, 0.0, wz/2) ])#this lattice has a limited size of 10 gratingsTx=esc.par("Period X", 100, units="nm")Ty=esc.par("Period X", 100, units="nm")latx = esc.lattice("", qx, Tx, 10)laty = esc.lattice("", qy, Ty, 10)I = esc.sas("", qx, qy, qz, V, latx*laty, multithread=True)show(I, coordinates=c, cblog=True, cbmin=1, rows=sz, plot_type="map", xlabel="Qx", ylabel="Qy")Width X[nm]:50.00Width Y[nm]:50.00Width Z[nm]:50.00Period X[nm]:100.0Period X[nm]:100.0Figure x=0.0975191 y=-0.0345939 [0.0144374]. . .