examples/notebooks/Optical_constants_ellipsometry_modelling.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.interpolate import InterpolatedUnivariateSpline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from solcore.absorption_calculator import calculate_ellipsometry\n",
    "from solcore.structure import Structure\n",
    "from solcore.data_analysis_tools.ellipsometry_analysis import EllipsometryData\n",
    "from solcore.graphing.Custom_Colours import colours\n",
    "from solcore.absorption_calculator.cppm import Custom_CPPB as cppb\n",
    "from solcore.absorption_calculator.dielectric_constant_models import Oscillator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "E_eV = np.linspace(0.7, 4.2, 1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load in ellipsomery data from file..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Exp_Data = EllipsometryData(\"../data/ge_ellipsometry_data.dat\")\n",
    "Exp_Angles = Exp_Data.angles"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load in some experimental Ge n-k to compare fit with this..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Ge_nk_Exp = np.loadtxt(\"../data/Ge_nk.csv\", delimiter=\",\", unpack=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Smooth the data with spline fitting..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_spline = InterpolatedUnivariateSpline(x=Ge_nk_Exp[::5, 0], y=Ge_nk_Exp[::5, 1], k=3)(E_eV)\n",
    "k_spline = InterpolatedUnivariateSpline(x=Ge_nk_Exp[::5, 2], y=Ge_nk_Exp[::5, 3], k=3)(E_eV)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Step 1 :: n and k modelling...<br>\n",
    "First model the Ge02 layer with the Sellmeier model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define Oscillator Structure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "GeO2 = Structure([\n",
    "    Oscillator(oscillator_type=\"Sellmeier\", material_parameters=None,\n",
    "               A1=0.80686642, L1=0.68972606E-1,\n",
    "               A2=0.71815848, L2=0.15396605,\n",
    "               A3=0.85416831, L3=0.11841931E2)\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "GeO2_nk = cppb().nk_calc(oscillator_structure=GeO2, energy_array=E_eV)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Step 2 :: use this modelled n and k to calculate the ellipsometry data...<br>\n",
    "Define a structure for the optical stack..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "stack = Structure([\n",
    "    [4.4, 1240 / E_eV, GeO2_nk[\"n\"], GeO2_nk[\"k\"]],  # Layer 1 :: GeO2 native oxide layer\n",
    "    [350000, 1240 / E_eV, n_spline, k_spline]  # Layer 2/ Substrate :: Bulk Ge\n",
    "])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate Ellipsometry data..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Out = calculate_ellipsometry(stack, 1240 / E_eV, angle=Exp_Angles)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define functions for the quick conversion of data<br>\n",
    "We show this with the angle = 79º, which is the third one (i = 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "i = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "rho = lambda psi, delta: np.tan(psi) * np.exp(1j * delta)\n",
    "eps = lambda r, theta: np.sin(theta) ** 2 * (1 + np.tan(theta) ** 2 * ((1 - r) / (1 + r)) ** 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Experimental data..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Exp_rho = rho(np.radians(Exp_Data.data[Exp_Angles[i]][1]), np.radians((Exp_Data.data[Exp_Angles[i]][3])))\n",
    "Exp_eps = eps(Exp_rho, np.radians(Exp_Angles[i]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Modelled data..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Mod_rho = rho(np.radians(Out[\"psi\"][:, i]), np.radians(Out[\"Delta\"][:, i]))\n",
    "Mod_eps = eps(Mod_rho, np.radians(Exp_Angles[i]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Step 3 :: Data Plotting..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax1 = plt.subplots(1, 1)\n",
    "ax1b = ax1.twinx()\n",
    "ax1.set_xlim([400, 1500])\n",
    "\n",
    "ax1.plot(Exp_Data.data[Exp_Angles[i]][0] * 1000, Exp_eps.real, lw=2, marker=\"o\", ls='none', color=colours(\"Orange Red\"),\n",
    "         label=\"$\\epsilon_1 (\\lambda)$ :: $ %3.1f^{\\circ}$\" % Exp_Angles[i])\n",
    "ax1b.plot(Exp_Data.data[Exp_Angles[i]][0] * 1000, abs(Exp_eps.imag), lw=2, marker=\"s\", ls='none',\n",
    "          color=colours(\"Dodger Blue\"),\n",
    "          label=\"$\\epsilon_2 (\\lambda)$ :: $ %3.1f^{\\circ}$\" % Exp_Angles[i])\n",
    "\n",
    "ax1.plot(1240 / E_eV, Mod_eps.real, label=\"Model $\\epsilon_1 (\\lambda)$ :: $ %3.1f^{\\circ}$\" % Exp_Angles[i],\n",
    "         color=colours(\"Maroon\"))\n",
    "ax1b.plot(1240 / E_eV, abs(Mod_eps.imag), label=\"Model $\\epsilon_2 (\\lambda)$ :: $ %3.1f^{\\circ}$\" % Exp_Angles[i],\n",
    "          color=colours(\"Navy\"))\n",
    "\n",
    "ax1.set_xlabel(\"Wavelength (nm)\")\n",
    "ax1.set_ylabel('$\\epsilon_1 (\\lambda)$')\n",
    "ax1b.set_ylabel('$\\epsilon_2 (\\lambda)$')\n",
    "ax1.text(0.05, 0.9, '(b)', transform=ax1.transAxes, fontsize=12)\n",
    "\n",
    "ax1.legend(loc=\"lower left\")\n",
    "ax1b.legend(loc=\"upper right\")\n",
    "\n",
    "plt.show()"
   ]
  }
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