{ "cells": [ { "cell_type": "markdown", "metadata": { "hideCode": false, "hidePrompt": false }, "source": [ "\n", "\n", " **Chapter 4: [Spectroscopy](CH4_00-Spectroscopy.ipynb)** \n", "\n", "
\n", "\n", "\n", "\n", "# Analysing Low-Loss Spectra with Drude Theory\n", "\n", "[Download](https://raw.githubusercontent.com/gduscher/MSE672-Introduction-to-TEM/main/Spectroscopy/CH4_03-Drude.ipynb)\n", "\n", " [![OpenInColab](https://colab.research.google.com/assets/colab-badge.svg)](\n", " https://colab.research.google.com/github/gduscher/MSE672-Introduction-to-TEM/blob/main//Spectroscopy/CH4_03-Drude.ipynb)\n", "\n", "\n", "part of \n", "\n", " **[MSE672: Introduction to Transmission Electron Microscopy](../_MSE672_Intro_TEM.ipynb)**\n", "\n", "\n", "**Spring 2026**
\n", "by Gerd Duscher\n", "\n", "Microscopy Facilities
\n", "Institute of Advanced Materials & Manufacturing
\n", "Materials Science & Engineering
\n", "The University of Tennessee, Knoxville\n", "Background and methods to analysis and quantification of data acquired with transmission electron microscopes.\n", "\n", "\n", "\n", "Background and methods to analysis and quantification of data acquired with transmission electron microscopes." ] }, { "cell_type": "markdown", "metadata": { "hideCode": false, "hidePrompt": false }, "source": [ "## Content\n", "The main feature in a low-loss EELS spectrum is the ``volume plasmon`` peak.\n", "\n", "This ``volume plasmon`` and all other features in the ``low-loss`` region of an EELS spectrum are described by Dielectric Theory of Electrodynamics.\n", "\n", "The simplest theory to interprete this energy range is the Drude theory. \n", "\n", "Another easy to observe component is the multiple scattering of this plasmon peak, which we can correct for or use for thickness determination.\n", "\n", "## Load important packages\n", "\n", "### Check Installed Packages\n" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "done\n" ] } ], "source": [ "import sys\n", "import importlib.metadata\n", "def test_package(package_name):\n", " \"\"\"Test if package exists and returns version or -1\"\"\"\n", " try:\n", " version = importlib.metadata.version(package_name)\n", " except importlib.metadata.PackageNotFoundError:\n", " version = '-1'\n", " return version\n", "\n", "if test_package('pyTEMlib') < '0.2026.1.0':\n", " print('installing pyTEMlib')\n", " !{sys.executable} -m pip install --upgrade pyTEMlib -q\n", "\n", "print('done')" ] }, { "cell_type": "markdown", "metadata": { "hideCode": false, "hidePrompt": false }, "source": [ "### Import all relevant libraries\n", "\n", "Please note that the EELS_tools package from pyTEMlib is essential." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "hideCode": false, "hidePrompt": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pyTEM version: 0.2026.1.0\n" ] } ], "source": [ "import sys\n", "%matplotlib ipympl\n", "if 'google.colab' in sys.modules: \n", " from google.colab import output\n", " from google.colab import drive\n", " output.enable_custom_widget_manager()\n", " \n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import scipy\n", "\n", "# Import libraries from the book\n", "import pyTEMlib\n", "\n", "# For archiving reasons it is a good idea to print the version numbers out at this point\n", "print('pyTEM version: ',pyTEMlib.__version__)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Dielectric Theory\n", "\n", "### Comparison to Optical Spectroscopy\n", "\n", "The interaction of a transmitted electron with a solid is here described in terms of\n", "a dielectric response function $\\varepsilon(q, \\omega))$. \n", "\n", "The same response function $\\varepsilon(q, \\omega))$ describes\n", "the interaction of any electro-magnetic wave (such as photons) with a solid, so this formalism allows energy-loss data to be compared with the results of optical measurements.\n", "\n", "The difference is that there is no momentum transfer in an optical transition and, therefore, the relevant dielectric function is $\\varepsilon(q=0, \\omega))$.\n", "\n", "\n", "The optical dielectric function (permittivity) is a transverse property of the medium, in the sense that the electric field of an electromagnetic wave displaces electrons in a direction perpendicular to the direction of propagation, the electron density remaining\n", "unchanged. \n", "\n", "The relation between the ac conductivity $\\sigma$ (for dc conductivity the in metals $\\varepsilon$ can go to $\\inf$ and is therefore not well described) and $\\varepsilon$ is :\n", "$$ \\varepsilon = 1 + \\frac{4\\pi \\ i \\sigma}{\\omega} $$\n", "\n", "The relation between the complex refractive index $n+i\\kappa$ and dielectric function is:\n", "$$ n^2-\\kappa^2 ={\\bf Re}(\\varepsilon), \\ \\ 2n\\kappa = {\\bf Im}(\\varepsilon) $$\n", "\n", "Optical absorption spectrum is obtained through\n", "ABS= ${\\bf Im}( \\varepsilon(q→0,\\omega) )$\n", "\n", ">\n", ">So, the dielectric function describes the electrical and optical response of a material almost completely. \n", ">\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Dispersion \n", "From the Fourier representation of the Maxwell equations in the source free case, we get:\n", "$$\\frac{\\epsilon_i \\mu_i}{c^2} = k^2$$\n", "\n", "which we transform into:\n", "\n", "$$k = \\frac{\\omega}{c} \\sqrt{\\varepsilon_1 \\mu}$$\n", "\n", "which gives for non-magnetic materials:\n", "\n", "$$k = \\frac{\\omega}{c} \\sqrt{\\varepsilon_1 }$$\n", "\n", "for $\\varepsilon_1 > 0$ the wavenumber $k$ is a real function of real $\\omega$.\n", "\n", "while for $\\varepsilon_1 < 0$ the wavenumber $k$ is purely imaginary.\n", "\n", "\n", "for light in vacuum the permittivity $\\varepsilon_1$ is a constant with value 1 and we get the equation for light line:\n", "\n", "$$k = \\frac{\\omega}{c}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Cross Section\n", "\n", "$$ \\frac{d^2\\sigma}{dE d\\Omega} = \\frac{1}{\\pi a_0 m_0 v^2 n_a} \n", " {\\rm Im} \\left[ \\frac{-1}{\\varepsilon(q,E)} \\right]\n", " \\left( \\frac{1}{\\theta^2+\\theta_E^2}\\right)$$\n", " \n", "The partial cross section $\\frac{d^2\\sigma}{dE d\\Omega}$ gives us the probability that an incident electron will be scattered into angle $q$ with energy-loss $E$.\n", "\n", "There are three compenents, first a term that depends on the ``atom density`` $n_a$ (atoms per volume).\n", "\n", "And the third term is the (Lorentzian) ``angle dependence`` with the characteristic angle $$\\theta_E = E_E/(\\gamma m_0v^2)$$\n", "\n", "The second term is the ``loss-function``.\n", "\n", "The loss function of a dielectric function $\\varepsilon = \\varepsilon_1+ i*\\varepsilon_2$ is\n", "$$ {\\rm Im} \\left[ \\frac{-1}{\\varepsilon(q,E)} \\right] = \\frac{\\varepsilon_1(q,E)}{\\varepsilon_1^2(q,E) + \\varepsilon_2^2(q,E)}$$\n", "At large energy loss and $q\\approx 0$, $\\varepsilon_2$ is small\n", "and $\\varepsilon_1$ close to 1, the loss function becomes proportional to\n", "$\\varepsilon_2$ and (apart from a factor of E$^{−3}$) the energy-loss spectrum is proportional to the X-ray absorption spectrum." ] }, { "cell_type": "markdown", "metadata": { "hideCode": false, "hidePrompt": false }, "source": [ "## Load and plot a spectrum" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# ---- Input ------\n", "load_example = True\n", "# -----------------\n", "if not load_example:\n", " if 'google.colab' in sys.modules:\n", " drive.mount(\"/content/drive\")\n", "\n", " fileWidget = pyTEMlib.file_tools.FileWidget()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "hideCode": false, "hidePrompt": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "frames: Number of frames\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "276580024dd24950a46e51ea5f9b0268", "version_major": 2, "version_minor": 0 }, "image/png": 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If the physical density of a\n", "material were reduced by a factor $f$, the scattering per atom would remain the same\n", "(according to an atomic model) and the mean free path should increase by a factor $f$.\n", "\n", "The big problem however, is that one has to know the **dielectric function**. \n", "In the case of the Drude theory, that means we need to know the electron density.\n", "\n", "Any approximation, therefore, needs to approximate this dielectric function, which cannot be generally applicable.\n", "\n", "\n", "The relative thickness $ t_{rel} = t/\\lambda$, in contrast, is relatively easy to determine. All the above problems are hidden in value of the inelastic mean free path (IMFP) $\\lambda$, which is the inverse of the cross section above.\n", "\n", "**When you use a tabulated value for the IMFP, be aware that this value depends on:**\n", "* acceleration voltage\n", "* effective collection angle\n", "* material density\n", " \n", ">**and may not be applicable for your experimental setup.**\n", "\n", "\n", "\n", "The measurement of the relative thickness $t_{rel}$ is relative easy:\n", "\n", "We already did this in the [Fit Zero-Loss](./CH4_02-Fit_Zero_Loss.ipynb) part.\n", "\n", "The inelastic scattering can be viewed in terms of independent collisions, whose occurrences obey Poisson statistics. The probability that a transmitted electron suffers $n$ collisions is \n", "\\begin{equation} \\Large\n", "P_n = (1/n!)m^n \\exp(-m)\n", "\\end{equation}\n", "\n", "where $m$ is the number of average collisions for electrons travel through this sample area. The number $m$ can be set to the scattering parameter $t/\\lambda$. $P_n$ is represented in the EELS spectrum by the ration of the energy-integrated intensity $I_n$ of $n$-fold scattering divided by the {\\bf total} integrated intensity $I_t$:\n", "\\begin{equation} \\Large\n", "P_n = I_n/I_t (1/n!) (t/\\lambda)^n \\exp(-t/\\lambda)\n", "\\end{equation}\n", "\n", "For a given order $n$ of scattering, the intensity is highest when $t/\\lambda =n$\n", "In the case of the unscattered (n=0) component (zero--loss peak), the intensity is highest at t=0 and decreases exponentially with specimen thickness. For $n=0$, equation \\ref{equ:poisson} gives equation \n", "\\begin{equation} \\Large\n", "\\frac{t}{\\lambda}= - \\ln\\left[ \\frac{I_{\\mbox{total}}}{I_{zl}}\\right]\n", "\\end{equation}\n", "I just replaced $I_{zl}$ with $I_0$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "hideCode": false, "hidePrompt": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Zero Loss with energy resolution of -0.15 eV at position -0.136 eV\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\gduscher\\AppData\\Local\\Temp\\ipykernel_52100\\539939054.py:4: DeprecationWarning: __array_wrap__ must accept context and return_scalar arguments (positionally) in the future. (Deprecated NumPy 2.0)\n", " eels_dataset.energy_loss -= energy_shift\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Sum of Zero-Loss: 1749 counts\n", "Sum of Spectrum: 100 counts\n", "thickness [IMFP]: -2.86143\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "0c69109875714ec5a94944461fc3dfbc", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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This results for thicknesses around 0.5 MFP in more intensity in the high energy tail of the plasmon peak. For thicker areas a second plasmon peak will appear at double the energy loss and for very thick areas we have a whole series of plasmon peaks.\n", "In spectra of very thick areas the zero-loss peak may completely vanish. Multiple scattering is easily recognized by the positions of the peaks (multiple of $E_{max}$).\n", "\n", "Multiple scattering influences the high energy side of the first plasmon peak, and makes it difficult to quantify the spectra, whether it is in the low-loss or core--loss region. Figure \\ref{fig:ssd} shows how the correction improves the determination of the width of the plasmon width. Fortunately, we can correct this multiple scattering, because mathematically, it is a kind of self-convolution. The procedure is called single scattering deconvolution (SSD).\n", "\n", "\n", "Electrons that lost energy can interact with the sample again. The average path between two interaction is the above introduced IMFP $\\lambda$. This multiple inelaxtic scattering is most obvious in the strongest energ-loss spectrum: the volume plasmon. This multiple scatering follows the Poisson statistic and the $n^{\\rm th}$ scattering has the intensity:\n", "$$I_n = I_0 P_n = (I_0/n!)(t/λ)^n \\exp(−t/λ)$$\n", "\n", "It can be shown the the single scattering spectrum in fourier space $s(v)$ can be derived by:\n", "\n", "$$s(v) = I_0 \\ln[j(v)/z(v)]$$\n", "\n", "$z(v)$ beeing the Fourier transformed zero-loss peak (resolution function) and $j(v$ the spectrum in Fourier space.\n", "\n", "The above formula would also correct for any instument broadening and a very noisy spectrum would result, so we need to convolute (multiplication in Fourier space) a new broadening function, which could be a well behaved Gaussian with slightly smaller energy width than the original zero-loss peak.\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "hideCode": false, "hidePrompt": false }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "82898eb0e2aa460fb17da731ed4aaba7", "version_major": 2, 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", 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These interactions, therefore, have a high intensity and are easy to obtain. The quantification of this region ($<$ 100eV) in an EELS spectrum is rather hard.\n", "\n", "The valence electrons in a solid can be considered as coupled oscillators which interact with each others and with the transmitted electrons. In a first approximation the valence electrons behave like a free electron gas (Fermi sea, jellium). The behavior of the electron gas is described in terms of the dielectric function $\\varepsilon$.\n", "\n", "\n", "The energy-loss function $F_{el}$ on the other hand is determined by the dielectric function $\\varepsilon$ through:\n", "\n", "$$\n", "F_{el} = \\Im \\left[\\frac{-1}{\\varepsilon(\\omega)} \\right]\n", "$$\n", "\n", "The maximum of the energy-loss function is the plasmon--peak, which is given by:\n", "$$\n", "E_{max} = \\left[(E_p)^2 - (\\Delta E_p/2)^2\\right]^{1/2}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Dielectric Theory\n", "\n", "We investigate the plasmon excitation in the so called jellium model. This model is enough to explain the essence of this excitation, but is not as complicated as the real solid state.\n", "\n", "\n", "The displacement of a {\\it quasifree} electron (with an effective mass $m$ and not the rest mass $m_0$) due to an electric field $\\vec{E}$ must fulfill the equation :\n", "\\begin{equation} \\Large\n", "m\\vec{x}'' + m\\Gamma \\vec{x}' = -e\\vec{E}\n", "\\end{equation}\n", "\n", "The usage of an effective mass approximates the interaction between the valence electrons and the ion--cores. For the same reason, we introduce $\\Gamma$ a damping constant. Instead of $\\Gamma$, we could also use its reciprocal value $\\tau = 1/\\Gamma$ as in the Drude theory. This is similar to the electronic theory of conduction.\n", "\n", "\n", "For an oscillatory field $\\vec{E}= \\vec{E} \\exp(-i\\omega t)$ above equation \\ref{equ:motion} has the following solution:\n", "\\begin{equation} \\Large\n", "\\vec{x} = (e\\vec{E}/m)(\\omega ^2+i\\Gamma \\omega)^{-1}\n", "\\end{equation}\n", "\n", "\n", "The displacement gives raise to a polarization $\\vec{P} = -en\\vec{x} =\\varepsilon_0\\chi\\vec{E}$, with $\\chi$ electric susceptibility and $n$ the the number of electron per unit volume. The dielectric function $\\varepsilon(\\omega)=1+\\chi$ can be expressed as:\n", "\\begin{equation} \\Large\n", "\\varepsilon(\\omega)=\\varepsilon_1+i\\varepsilon_2 = 1-\\frac{\\omega_p^2}{\\omega^2+\\Gamma^2}+\\frac{i\\Gamma\\omega^2_p}{\\omega(\\gamma^2+\\Gamma^2)}\n", "\\end{equation}\n", "Where $\\omega$ is the frequency (in rad/s) of forced oscillation and $\\omega_p$ is the Eigen or resonance frequency of the free electron gas, which is given by:\n", "\\begin{equation} \\Large\n", "\\omega_p =\\left[ \\frac{ne^2}{\\varepsilon_0 m} \\right]^{1/2}\n", "\\end{equation}\n", "\n", "\n", "A sudden impulse such as a transmitted electron will contain all angular frequencies (Fourier components). It will also excite the resonance frequency of the jellium. Such an oscillation with frequency $\\omega_p$ can be viewed as a ``pseudoparticle`` with (plasmon) energy $E_p =\\hbar \\omega_p.$ We call this ``pseudoparticle`` a **plasmon**." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Energy-Loss Function\n", "The energy-loss function (elf) is given as shown in the beginning by:\n", "\\begin{equation} \\Large\n", "E_{el}= \\left[\\frac{1}{\\varepsilon(\\omega)}\\right] = \\frac{\\varepsilon_2}{\\varepsilon_1^2+\\varepsilon_2^2}=\\frac{\\omega\\Gamma\\omega_p^2}{(\\omega^2-\\omega_p^2)^2 +(\\omega\\Gamma)^2}\n", "\\end{equation}\n", "The energy-loss is represented by $E=\\hbar \\omega$ and we can rewrite equation \n", "\\ref{equ:eels_function2} as:\n", "\\begin{equation}\n", " \\left[\\frac{1}{\\varepsilon(E)}\\right] =\\frac{(E\\hbar/\\tau)E_p^2}{(E^2-E^2)^2 +(E\\hbar/\\tau)^2} %\n", " =\\frac{(E \\quad \\Delta E_p)E_p^2}{(E^2-E^2)^2 +(E \\quad \\Delta E_p)^2} \n", "\\end{equation}\n", "\n", "\n", "The relaxation time $\\tau = 1/\\Gamma$ is directly connected to the FWHM of the energy-loss function which is given by $\\Delta E_p =\\hbar\\Gamma = \\hbar/\\tau$. The effect of the effective mass on the energy-loss function is rather small.\\\\ \n", "The maximum of the energy-loss function is given in equation \\ref{equ:plasmon-maximum}.\n", "\n", "\n", "The relaxation time $\\tau$ represents the time for plasmon oscillations to decay in energy by a factor $\\exp(-1)=0.37$. The number of oscillations which occur within this time is $\\omega_p\\tau/(2\\pi)=E_p/(2\\pi/\\Delta E_p)$. Using experimental values for $E_p$ and $\\Delta E_p$ result in 5 to 0.4 oscillations. The plasmon oscillations are, therefore, heavily damped, which depends on the band structure of the material. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plasmon Energies\n", "\n", "The calculated plasmon energies of the Jellium model with equation \\ref{equ:plasmon_frequency} are already quite good as can be seen in table \\ref{tbl:plasmon_frequencies}.\n", "Only the number of valence electrons per unit area $n$ and the dielectric constant $\\varepsilon_0$ are necessary for these calculations.\n", "\n", "\n", "\n", "| Material | $E_p$ (experimental) | $E_P$ (theoretical)|\n", "|----------|-----------------------|--------------------|\n", "|Li | 7.1 eV | 8.0 eV|\n", "|Diamond | 34 eV | 31 eV|\n", "|Si | 16.5 eV | 16.6 eV| \n", "|Ge | 16.0 eV | 15.6 eV|\n", "|InSb | 12.9 eV | 12.7 eV|\n", "|GaAs | 15.8 eV | 15.7 eV|\n", "|NaCl | 15.5 eV | 15.7 eV|\n", "\n", "A more sophisticated way of comparing the valence loss spectra to theory is to calculate the dielectric function. {\\it Ab initio} density functional theory can be used to do these calculations. To obtain the dielectric function the valence band has to be convoluted with the conduction band. A comparison between experiment and theory is shown in the figure below. \n", "\n", "\"Plasmon--Loss\n", "\n", "*Plasmon--Loss peak of Li (black circles), Gibbson et al Phys.~Rev.~B {\\bf 13}:2451 (1979) and calculated energy-loss function by S.~Ramachandran et al. (unpublished)}*\n", "\n", "The plasmon--loss enables us to determine the plasmon energy, a materials parameter.\n", "The width plasmon peak is also a characteristic of the material and is needed to determine the plasmon energy.\n", "\n", "\"Plasmon-loss\"\n", "\n", "*Plasmon--Loss peak of SrTiO$_3$ with highlighted FWHM*\n", "\n", "The spectrum here is quite complicated due to the surface plasmon--peak which shows up to the left of the volume plasmon--peak. We measure the energy of the maximum of the plasmon--peak (here $E_{\\mbox{max}} = 31$ eV) and the width of the plasmon--peak (here $\\Delta E_P = 5.3$ eV). While it is easy to determine the plasmon--peak energy , the plasmon--peak width can only be determined approximately, because we don't know how to subtract the background.\n", "\n", "Using equation above, we find that the plasmon energy is 30.5 eV for SrTiO$_3$.\n", "\n", "\n", "\n", "This spectrum shows the high dynamic range of an EELS spectrum. The valence loss part of the spectrum is noisy, but the zero-loss peak is not saturated. The surface plasmon peak is strong, which indicates a rather thin area. May be a little too thin. Without loss of information we can get spectra from thicker areas.\n", "\n", "\n", "Not only the plasmon energy (or the plasmon maximum) can be used for an identification of materials,\n", "but also the shape, especially the width of the plasmon peak.\n", "\n", "As seen above, it is rather difficult to determine the FWHM of a plasmon peak. However, it is much easier after subtraction of the zero-loss peak, as can be seen in figure below.\n", "\n", "\"Ni\n", "\n", "*Plasmon--Loss peak of Ni (black) after subtraction of the zero-loss peak and with highlighted FWHM. The original spectrum and the zero-loss peak are displayed in the background.*\n", "\n", "A comparison of the plasmon peak width of Ni (above) and Si (figure below)\n", " makes it apparent how different the shape of plasmon peaks can be. The Si plasmon peak is sharp (FWHM: 7.3 eV) and has a well defined maximum, while the Ni plasmon peak is very broad (FWHM: 40 eV).\n", "\n", "\"Si\n", "*Plasmon--Loss peak of Si (black) after subtraction of the zero-loss peak and with highlighted FWHM. The original spectrum and the zero-loss peak are displayed in the background.*\n", "\n", "The Si plasmon peak is obtained from a rather thin area, which also makes it easier to determine the width, because the right hand tail is not broadened by the thicker sample (please see section above about single scattering deconvolution). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Drude Function\n", "\n", "The dielectric function in the Drude theory is given by two input parameters the position of the plasmon energy $E_p$\n", "and the width of the plasmon $\\Gamma$\n", "\n", "$$ ε(ω) = ε1 + iε2 = 1 + χ = 1 − \\frac{\\omega_p^2}{\\omega^2+\\Gamma^2} + \\frac{i\\Gamma \\omega_p^2}{\\omega(\\omega^2+\\Gamma^2)}$$\n", "Here $\\omega$ is the angular frequency (rad/s) of forced oscillation and $\\omega_p$ is the natural or resonance frequency for plasma oscillation, given by\n", "$$ ω_p = \\sqrt{\\frac{ne^2}{(ε_0m_0)}} $$\n", "A transmitted electron represents a sudden impulse of applied electric field, containing\n", "all angular frequencies (Fourier components). Setting up a plasma oscillation of the loosely bound outer-shell electrons in a solid is equivalent to creating a pseudoparticle of energy $E_p = \\hbar \\omega_p$, known as a plasmon (David Pines, Elementary Excitations in Solids, 1963)." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\gduscher\\AppData\\Local\\Temp\\ipykernel_52100\\1991494804.py:5: DeprecationWarning: __array_wrap__ must accept context and return_scalar arguments (positionally) in the future. (Deprecated NumPy 2.0)\n", " energy_scale = eels_dataset.energy_loss+1e-18 #= np.linspace(0,50,1024)+1e-18\n" ] }, { "data": { "text/plain": [ "Text(0.5, 0, 'energy loss (eV)')" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "e643eaaef742419cbf2b6bc843c220c1", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# ----------- Input -------------\n", "E_p = plasmon_energy = 17. # in eV\n", "E_w = plasmon_gamma = .7 # in eV\n", "# -------------------------------\n", "energy_scale = eels_dataset.energy_loss+1e-18 #= np.linspace(0,50,1024)+1e-18\n", "\n", "\n", "def Drude(E,E_p,E_w):\n", " eps = 1 - E_p**2/(E**2+E_w**2) +1j* E_w* E_p**2/E/(E**2+E_w**2)\n", " elf = (-1/eps).imag\n", " return eps,elf\n", "\n", "eps,elf = Drude(np.array(energy_scale), plasmon_energy, plasmon_gamma)\n", "\n", "plt.figure()\n", "plt.plot(energy_scale, eps.real, label='Re($\\epsilon_{Drude}$)')\n", "plt.plot(energy_scale, eps.imag, label='Im($\\epsilon_{Drude}$)')\n", "plt.plot(energy_scale, elf, label='loss function$_{Drude}$')\n", "plt.plot([0,energy_scale[-1]],[0,0],c='black')\n", "\n", "plt.legend()\n", "plt.gca().set_ylim(-2,max(elf)*1.05);\n", "plt.xlabel('energy loss (eV)')" ] }, { "cell_type": "markdown", "metadata": { "hideCode": false, "hidePrompt": false }, "source": [ "## Fitting a Drude Function to Plasmon\n", "\n", "The position and the width are important materials parameters and we can derive them by fitting the Drude function to the volume plasmon region." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "hideCode": false, "hidePrompt": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Drude Theory with Plamson Energy: 15.049 eV and plasmon Width 0.70 eV\n", "Max of Plasmon at 15.043 eV\n", "Amplitude of 0.01 was determined by fit \n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "c06146a056b7465da463b948b3e34129", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def Drude(E,Ep,Ew):\n", " eps = 1 - Ep**2/(E**2+Ew**2) +1j* Ew* Ep**2/E/(E**2+Ew**2)\n", " elf = (-1/eps).imag\n", " return eps,elf\n", "\n", "def errfDrude(p, y, x):\n", " eps, elf = Drude(x,p[0],p[1])\n", " err = y - p[2]*elf\n", " return np.abs(err)\n", "\n", "\n", "starting_guess = np.array([15, 1, 0.1])\n", "start_channel = np.searchsorted(energy_scale.values, 13)\n", "end_channel = np.searchsorted(energy_scale.values, 18)\n", "\n", "fitted_values, lsq = scipy.optimize.leastsq(errfDrude, starting_guess, args=(eels_dataset[startFit:endFit], energy_scale.values[startFit:endFit]), maxfev=2000)\n", "\n", "eps, elf =Drude(np.array(energy_scale),fitted_values[0],fitted_values[1])\n", "drudePSD = fitted_values[2]* elf\n", "plt.figure()\n", "\n", "plt.plot(energy_scale,eels_dataset)\n", "plt.plot(energy_scale,drudePSD)\n", "plt.plot(energy_scale,eels_dataset-drudePSD)\n", "plt.axhline(0, color='black')\n", "\n", "plt.gca().set_xlim(0,40)\n", "plt.gca().set_ylim(-0.01,0.2)\n", "print(f\"Drude Theory with Plamson Energy: {fitted_values[0]:.3f} eV and plasmon Width {fitted_values[1]:.2f} eV\") \n", "print(f\"Max of Plasmon at {energy_scale[drudePSD.argmax(0)]:.3f} eV\")\n", "print(f\"Amplitude of {fitted_values[2]:.2f} was determined by fit \")\n" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "hideCode": false, "hideOutput": true, "hidePrompt": false }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "394e3ce6ecb24d78836dda6c51d982a5", "version_major": 2, "version_minor": 0 }, "image/png": 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\n", " Figure\n", "
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\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.title ('Drude Fit: Dielectric Function - Permittivity')\n", "plt.plot(energy_scale,eps.real,label = 'Re($\\epsilon)$')\n", "plt.plot(energy_scale,eps.imag,label = 'Im($\\epsilon)$')\n", "plt.plot(energy_scale,drudePSD,label = 'loss-function$_{Drude}$')\n", "plt.plot(energy_scale,eels_dataset,label = 'loss-function$_{exp}$')\n", "plt.axhline(0, color='black')\n", "\n", "plt.gca().set_xlim(0,20)\n", "plt.gca().set_ylim(-2.5,5.3)\n", "\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plasmon Frequency and Phase Identification\n", "\n", "\n", "Plasmon peaks occurring in EELS is directly related to valence electron density and can thereby be used as a means for materials characterization and phase identification. Free-electron metals have very sharp plasmon peaks as compared to semiconductors and insulators with broader peaks, where the valence electrons are no longer free (covalent or ionic bonding). While many materials properties are a function of valence electron density, knowing the plasmon energy can prove to be a useful tool in identifying micro structures.\n", "\n", "\n", "Microstructural phases are observed by shifts in the plasmon energy. Examples of phase identification are observed easily in alloys and also precipitate structures. A common textbook example is EELS low loss comparison of diamond and graphite. The example given in Figure is a line scan showing the variation of plasmon energies with position. The plasmon energies range from 21 to 23 eV, corresponding to SiC (20.8 eV) and SiN3 (22.5 eV) respectively. Figure \\ref{plasmon-ls2} is a reconstructed map of the plasmon energies. Blue regions correspond to SiC, while the red regions correspond to SiN3. \n", " \n", " \n", "Appendix C in Egerton's Electron Energy Loss Spectroscopy in the Electron Microscope lists plasmon energies of some elements and compounds [Egerton-1999]." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Surface Plasmon\n", "\n", "Spectra from thin specimen show the excitations of the surface plasmons on each side of the specimen. For any normal specimen these surface plasmons do interact, but this is not true for extremely thick specimen ($>> 10$nm).\n", "The surface plasmon frequency $\\omega_S$ for thin specimen is related to the bulk plasmon frequency $\\omega_P$ by Ritchie [Ritchie-PR1957]: \n", "$$\n", "\\omega_S=\\omega_P\\left[ \\frac{1\\pm \\exp(-q_st) }{1+\\varepsilon} \\right]^{1/2}\n", "$$\n", "\n", "\n", "The symmetric mode, where like charges face one another, corresponds to the higher angular frequency $q_s$. Please note, that this relationship does only apply for large $q_s$\n", "\n", "The differential probability for surface excitation at both surfaces of a sample with thickness $t$ can be expressed (normal incident, no retardation effects) by:\n", "$$\n", "\\frac{d^2 P_s}{d\\Omega d E}=\\frac{2\\hbar}{\\pi^2 \\gamma a_0 m_0^2 \\mu^3}\\frac{\\theta}{(\\theta^2+\\theta^2_E)^2} \\Im\\left[ \\frac{(\\varepsilon_a - \\varepsilon_b)^2 } {\\varepsilon_a^2 \\varepsilon_b}\\right]\n", "$$\n", "with \n", "$$\n", "R_c = \\frac{\\varepsilon_a \\sin^2(tE/2\\hbar\\mu)}{\\varepsilon_b + \\varepsilon_z }\\tanh (q_s t/2) \n", "+ \\frac{\\varepsilon_a \\cos^2(tE/2\\hbar\\mu)}{\\varepsilon_b + \\varepsilon_a} \\coth (q_s t/2) \n", "$$\n", "and $\\varepsilon_a$ and $\\varepsilon_b$ are the permitivities of the two surfaces.\n", "\n", "\n", "A secondary effect of the surface excitation is the reduced intensity of the bulk plasmon peak. The effect is usually smaller than 1\\%, but can be larger for spectra with small collection angle, because the preferred scattering of surfuce losses into small angles.\n", "The correction for surface plasmon will be discussed in the Kramers--Kronig Analysis.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Summary\n", "\n", "The beauty of ``Low--Loss spectroscopy`` is its derivation of the dielectric function to high energies without prior knowledge of the composition. The signal is strong and the acquisition time is mostly restricted by the dynamic range of the spectrum.\n", "\n", "\n", "**Think of low-loss spectroscopy as Electrodynamics**\n", "\n", "The advantages of EELS is the derivation of these values spatially resolved.\n", "And from a linescan across an Si/SiO$_2$ interface the dielectric function per pixel can be obtained. From that we can calculate the dielectric polarizability $\\alpha_e (E)$, which may be a measure of the dielectric strength.\n", "\n", "\n", "We obtain more or less easily:\n", "- relative thickness\n", "- absolute thickness \n", "- inelastic mean free path\n", "- plasmon frequency\n", "- plasmon width\n", "- band gap\n", "- dielectric function\n", "- reflectivity \n", "- absorption\n", "- effective number of electrons per atoms \n", " \n", "\n", "\n", "The analysis of the optical data requires the exact knowledge of the zero-loss peak. Because of the weighting in the Fourier Analysis, the low energy part contributes heavily to the dielectric function. Therefore, energy resolution is critical for an exact determination of all the optical values from EELS. The new monochromated TEMs are now able to achieve an energy resolution of 10 meV (one is at the oak Ridge National Laboratory), which allows for a sharper zero-loss peak. Such a sharp zero-loss peak will enable us to extract this low energy data more accurately. The dielectric function and the parameters derived from it, can be more precisely determined from such EELS spectra.\n" ] }, { "cell_type": "markdown", "metadata": { "hideCode": false, "hidePrompt": false }, "source": [ "## Navigation\n", "- **Up Chapter 4: [Imaging](CH4_00-Spectroscopy.ipynb)** \n", "- **Back: [Zero-Loss](CH4_02-Fit_Zero_Loss.ipynb)** \n", "- **Next: [Introduction to Core-Loss](./CH4_07-Introduction_Core_Loss.ipynb)** \n", "- **List of Content: [Front](../_MSE672_Intro_TEM.ipynb)** " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "hide_code_all_hidden": false, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.5" }, "toc": { "base_numbering": "3", "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": true }, "vscode": { "interpreter": { "hash": "838e0debddb5b6f29d3d8c39ba50ae8c51920a564d3bac000e89375a158a81de" } } }, "nbformat": 4, "nbformat_minor": 4 }