Electron probe microanalysis

Electron probe microanalysis
UW- Madison Geoscience 777 Electron probe microanalysis Electron - Specimen Interactions Revised 1/25/2018

What’s the point? Electrons from a source (“electron gun”)
UW- Madison Geology 777 What’s the point? Electrons from a source (“electron gun”) interact with atoms in specimen yielding a variety of photons and electrons via elastic and inelastic scattering processes. These are the “signals” that we use to make images and measure to characterize the composition of our specimens.

Electron-beam instrument
UW- Madison Geology 777 Electron-beam instrument A fixed (probe) or rastered (scanned) beam (SEM) of high energy electrons interacts with the atoms in the sample, yielding backscattered electrons, secondary electrons, auger electrons, and in some cases photons in the visible light range (CL). It is nominally non-destructive.

Overview Scattering Processes: Elastic and inelastic
UW- Madison Geology 777 Overview Scattering Processes: Elastic and inelastic Characteristic and continuum X-rays K,L,M etc: families of X-rays Energy versus wavelength Moseley’s relation Absorption or critical excitation energy Interaction volume and ranges Monte Carlo models of electron scattering Probability of X-ray production Distinction between X-rays and electrons

Elastic and inelastic scattering of HV electron by sample
UW- Madison Geology 777 Elastic and inelastic scattering of HV electron by sample Elastic (a): incident electron’s direction altered by Coulombic field of nucleus (Rutherford scattering), screened by orbital electrons. Direction may be changed by 0-180° (ave 2-5°) but velocity remains virtually constant. <1 eV of beam energy transferred. If exit the sample, then called BSEs. Inelastic (b): incident electron transfers some energy (up to all, E0) to tightly bound inner-shell electrons and loosely bound outer-shell electrons. Direction barely changes (<0.1°) E0 = accelerating voltage (of electrons emitted from gun); usually keV (Goldstein et al, 1992, p.72)

UW- Madison Geology 777 kV or keV? You may notice different terminology throughout these lectures, sometimes I say “kV” and sometimes “keV”…. Does it matter? Yes and no…. kV refers to a potential difference of the electric field, such as in a power supply or between the cathode and anode of the “electron gun” keV refers to the energy of the accelerated electron, such that an electron in a potential field will have a particular energy given by that field

Elastic and inelastic scattering of HV electron by sample
UW- Madison Geology 777 Elastic and inelastic scattering of HV electron by sample This Monte Carlo program output represents 1000 electron trajectories (idealized), in a cross-section--both elastic and inelastic scattering. Twenty years ago this took a fair amount of computing power…. (Goldstein et al, 1992, p.72)

Monte Carlo simulations are very useful
UW- Madison Geology 777 Monte Carlo simulations are very useful Today, you can simulate the “interaction volume” of scattered electrons for whatever kV and whatever composition material you may be interested in, in seconds. (above: using “CASINO” which you will be running on your computers soon) Gopon et al, 2013

Interaction Volume: critical concept
UW- Madison Geology 777 Interaction Volume: critical concept The volume where the incident high energy electrons scatter and generate X-rays = “interaction volume”. It can be MUCH larger than the footprint of the beam “spot” upon the initial “landing zone”. ! Critical Information Slide ! Gopon et al, 2013

Scattering vocabulary
UW- Madison Geology 777 Scattering vocabulary Cross section: a measure of the probability that an event of a certain kind will occur, e.g. K-shell cross section. Defined as Q = N/nint, where N=events of certain type/vol (sites/cm3), ni=number incident particles/unit area (particles/cm2), and nt=number target sites/vol (sites/cm3). Q has units of cm2 and is thought of as an effective ‘size’ which the atom presents as a target to incident particle. The Q for elastic scattering is ~10-17 cm2 and for K-shell ionization is ~10-20 cm2. Mean free path: average distance an electron travels within a specimen between events of a specific type. MFP=A/(NArQ) where A is atomic wt (g/mol), NA is Avogadro’s number (particles/mol), r is density (g/cm3).

Elastic and inelastic scattering
UW- Madison Geology 777 Elastic and inelastic scattering Elastic : Backscattering of electrons (~high energy) Inelastic : Secondary electron excitation (valence electrons) Inner-shell ionization (Auger electrons, X-rays) Bremsstrahlung (continuum) X-ray generation Cathodoluminescence radiation (non-metal valence shell phenomenon = light) Plasmon excitation (in metals, loosely bound outer-shell/ free electrons are excited) Phonon excitation (lattice oscillations: heating)

Backscattered Electrons
UW- Madison Geology 777 Backscattered Electrons High energy beam electrons may suffer single or multiple elastic scattering events in the solid, escaping from the material. The fraction of beam electrons that scatter back (h) was found experimentally to vary directly as a function of composition (atomic number Z). This provides a valuable imaging tool: a rapid means to discriminate phases that have different mean Z values. Intensity (grey level) varies from black (voids/epoxy), to plagioclase, olivine, basaltic glass, with Ti-magnetite the brightest phase.

UW- Madison Geology 777 Secondary Electrons Inelastic scattering of HV beam electron can promote loosely bound electrons from valence to conduction band in semiconductor or insulator with enough energy to move thru the solid (in metals, promotion from conduction-band directly). Backscattered electrons can also produce secondary electrons. By definition, these secondary electrons are <50 eV, with most <10 eV. a) Complete energy distribution of electrons emitted from target. Region I and II are BSE, Region III secondary. b) Secondary electron energy distribution, measured (points) and modeled (lines) (Goldstein et al, 1992, p. 107)

UW- Madison Geology 777 SE images – 3D! Secondary electrons are generated throughout the interaction volume, but only secondary electrons produced near the surface are able to escape (~5 nm in metals, ~50 nm in insulators). For this reason, secondary electron imaging (SEI) yields high resolution images of surface features. These intensitis are shown on a grey scale, though pseudo-coloring is sometimes done. 20 mm Pollen, cat flea, and Si nanowires on alumina sphere.

SE and BSE coefficients
UW- Madison Geology 777 SE and BSE coefficients Coefficients (fractions of total indicent beam electrons) for backscattered-electron (h) and secondary electron (d) as function of Z. Tilt of specimen from 90° beam incidence (q) is E0=30 keV. Data from 1966; more recent views suggest the flat SE curve may be due to carbon contamination on specimen hindering SE escape. (Goldstein et al, 1992, p. 109)

Inner-shell ionization: Production of X-ray or Auger e-
UW- Madison Geology 777 Inner-shell ionization: Production of X-ray or Auger e- K shell L shell (=photoelectron) Blue Lines indicate subsequent times: 1 to 2, then 3 where there are 2 alternate outcomes Time 1 2 3 HV electron knocks inner shell (K here) electron out of its orbit (time=1). This is an unstable configuration, and an electron from a higher energy orbital (L here) ‘falls in’ to fill the void (time=2). There is an excess of energy present and this is released internally as a photon. The photon has 2 ways to exit the atom (time=3), either by ejecting another outer shell electron as an Auger electron (L here, thus a KLL transition), or as X-ray (KL transition). (Goldstein et al, 1992, p 120)

UW- Madison Geology 777 X-ray Lines - K, L, M Ka X-ray is produced due to removal of K shell electron, with L shell electron taking its place. Kb occurs in the case where K shell electron is replaced by electron from the M shell. La X-ray is produced due to removal of L shell electron, replaced by M shell electron. Ma X-ray is produced due to removal of M shell electron, replaced by N shell electron. (Goldstein et al, 1992, p 121)

All possible K, L, M X-ray Lines
UW- Madison Geology 777 All possible K, L, M X-ray Lines (Originally Woldseth, 1973, reprinted in Goldstein et al, 1992, p 125)

X-ray Lines with initial + final levels
UW- Madison Geology 777 X-ray Lines with initial + final levels NB:not Greek! L N L L (Reed, 1993)

Nomenclature of X-rays
UW- Madison Geology 777 Nomenclature of X-rays There is some movement now to change the way X-rays are described, from the traditional Siegbahn notation (e.g. Ka1) to the the IUPAC (K-L3). (International Union of Pure and Applied Chemistry). This table is from their 1991 recommendation. (Reed, 1993)

X-ray energies, Cu for example
UW- Madison Geology 777 X-ray energies, Cu for example L3 2p3/ ev L2 2p1/ ev L1 2s ev K K2 K 1s ev Where do the values for characteristic x-rays come from: here are the numbers for Cu K x-rays: Subtract the energy of the L shell (binding) energy from that of the K shell (binding) energy, and you have the characteristic value. - 933 = 8046 eV (book says 8048) = 8027 eV (book says 8028)

Or… Fe L lines Ll = M1-L3 = 615.2 eV Lα1= M5-L3 = 705.0 eV
UW- Madison Geology 777 Or… Fe L lines Ll = M1-L3 = eV Lα1= M5-L3 = eV Lβ1= M4-L2 = eV (Gopon et al., 2013)

Absorption Edge Energy
UW- Madison Geology 777 Absorption Edge Energy Edge or Critical ionization energy: minimum energy required to remove an electron from a particular shell. Also known as critical excitation energy, X-ray absorption energy, or absorption edge energy. It is higher than the associated characteristic (line) X-ray energy; the characteristic energy is value measured by our X-ray detector. Example: Pt (Z=78) X-ray line energies and associated critical excitation (absorption edge) energies, in keV

Absorption Edge Energy
UW- Madison Geology 777 Absorption Edge Energy Edge or Critical ionization energy: minimum energy required to remove an electron from a particular shell. Also known as critical excitation energy, X-ray absorption energy, or absorption edge energy. It is higher than the associated characteristic (line) X-ray energy; the characteristic energy is value measured by our X-ray detector. Example: Pt (Z=78) X-ray line energies and associated critical excitation (absorption edge) energies, in keV ! Critical Information Slide !

UW- Madison Geology 777 Overvoltage Overvoltage is the ratio of accelerating (gun) voltage to critical excitation energy for particular line*. U = E0/Ec Maximum efficiency (cross-section) is at 2-3x critical excitation energy. Example of Overvoltage for Pt: for efficient excitation of this line, would be (minimally) thisß accelerating voltage La keV Ma -- 4 keV Example: Pt (Z=78) X-ray line energies and associated critical excitation (absorption edge) energies, in keV * recall: E0=gun accelerating voltage; Ec=critical excitation energy

UW- Madison Geology 777 Fluorescence yield Fluorescence yield (w) is fraction of ionizations that yield characteristic X-ray versus Auger yield (a) within a particular family of X-rays. w + a =1. Theoretically important, but in practice less so... (Goldstein et al, 1992)

Fluorescence yield alone … can cause misunderstanding
UW- Madison Geology 777 Fluorescence yield alone … can cause misunderstanding These are fractions, so each one is normalized to one. You cannot say anything about absolute detected x-ray intensities. 2. Practically: Measured characteristic x-rays by WDS will additionally be a function of (a) the crystal diffraction efficiency, (b) the gas absorption efficiency, and c) the spectrometer position (distance between detector and sample). For example, from the above chart, you cannot predict whether (Z=72) Hf La or Hf Ma will have higher count rates. (Ma, not La, have higher counts under normal conditions.)

UW- Madison Geology 777 Continuum X-rays HV beam electrons can decelerate in the Coulombic field of the atom (+ field of nucleus screened by surrounding e-). The loss in energy as the electron brakes is emitted as a photon, the bremsstrahlung (“braking radiation”). The energy emitted in this random process varies up from 0 eV to the maximum, E0. On an EDS plot of X-ray intensity vs energy, the continuum intensity decreases as energy increases. The high energy value where the continuum goes to zero is known as the Duane-Hunt limit. Duane-Hunt Limit The Duane-Hunt limit is very important to remember -- and utilize continuously! ! Critical Information Slide !

UW- Madison Geology 777 Kramer’s Law Duane-Hunt Limit Kramer’s Law (or Relation) is a mathematical description (formula) for the background or continuum shape and intensity: I = constant x Z (E0 - E) / E Where I is the intensity of the continuum at any energy E, Z is atomic number and E0 is the accelerating voltage

Continuum and Atomic Number
UW- Madison Geology 777 Continuum and Atomic Number At a given energy (or l), the intensity of the background (continuum) increases directly with Z (atomic number) of the material. This is the basis for a timesaving technique (Mean Atomic Number,“MAN”). Here the SX51 is counting X-rays in a limited range of the spectrum where there are no characteristc X-ray lines, we see only the continuum. Notice how the intensities rise with increasing atomic number of these metals.

Continuum and Atomic Number
UW- Madison Geology 777 Continuum and Atomic Number We can plot the background (continuum) intensity versus atomic number (Z), and see it is a well defined line/curve. This nice “MAN” relationship means that it is possible to deduce the correct background intensity without explicitly measuring it (with the proper software). This is a time-saver.

X-ray units: A, keV, sin q, mm
UW- Madison Geology 777 X-ray units: A, keV, sin q, mm l = hc/E0 where h=Plancks constant, c=speed of light l = /E0 where l is in Å and E0 in keV also, the 2 main EMPs plot up X-ray positions thusly: Cameca: n l = 2d sin q so for n=1 and a given 2d, an X-ray line can be given as a sin value (or 105 times sin q) JEOL: distance (L, in mm) between the sample (beam spot) and the diffracting crystal, i.e. L= l R/d, where R is Rowland circle radius (X-ray focusing locus of points) and d is interlayer spacing of crystal.

Henry Mosley (1887-1915) and Mosley’s Law
X-ray lines detected on photographic film, positioned in order of wavelength diffracted

Henry Mosley (1887-1915) and Mosley’s Law
X-rays are ordered in wavelength (=energy) l =B/(Z-C)2, where B and C are constants for each family of X-rays.

Using X-rays for Chemical Characterization
X-rays are ordered in wavelength (=energy) = CHACTERISTIC and X-ray intensity is proportional (roughly) to the elemental abundance in a compound

Cathodoluminesce When insulators and semiconductors are hit by HV electrons, long l photons (UV, visible, IR light) may be emitted. The light may be bright enough to be seen in the reflected light image (examples are benitoite, scheelite, zircon, corundum, diamond, wollastonite, YAG, GaAlAs). Incident electrons may promote valence shell electrons across the band gap to the empty conduction band, creating electron-hole pairs. With no bias to sweep the electron away, it will recombine with the hole. The excess energy (= gap energy) will be emitted as a long wavelength (=low energy, around 1 eV) photon... which is the wavelength/energy of visible (and near visible) light.

CL Images UW- Madison Geology 777 Impurity atoms as well as dislocations increase the possibilities for additional gap energies, yielding different wavelengths of emitted light.These may be valuable for production of diagnostic images. CL is a cheap way to view overgrowths (inherited cores) and healed fractures in quartz and zircons. CL image of zircon from Yellowstone tephra (Lava Creek Tuff). Note faint oscillatory zoning surrounding sector-zoned core, and healed fractures. These are not visible in the BSE image. ~50 um grain. (courtesy Ilya Bindeman)

Electron interaction volumes
Effect of beam interaction (damage) in plastic (polymethylmethacrylate), from Everhart et al., All specimens received same beam dosage, but were etched for progressively longer times, showing in (a) strongest electron energies, to (g) the region of least energetic electrons. Note teardrop shape in (g). Same scale for all. (Goldstein et al, 1992, p 80)

Ranges and interaction volumes
UW- Madison Geology 777 Ranges and interaction volumes It is useful to have an understanding of the distance traveled by the beam electrons, or the depth of X-ray generation, i.e. specific ranges. For example: If you had a 1 um thick layer of compound AB atop substrate BC, is EPMA of AB possible?

Electron and X-ray Ranges
Several researchers have developed physical/mathematical expressions to approximate electron and X-ray ranges. Two common ones are given below. Electron range. Kanaya and Okayama (1972) developed an expression for the depth of electron penetration: RKO=( A E01.67)/(r Z0.89) X-ray range. Anderson and Hasler (1966) give the depth of X-ray production as: RAH=(0.064)(E Ec1.68)/ r where Ec is the absorption edge (critical excitation) energy. There are nomograms for these ranges, given on the next slide.

Ranges From Will Bigelow, now emeritus U MI (Ann Arbor)
UW- Madison Geology 777 Ranges From Will Bigelow, now emeritus U MI (Ann Arbor)

Monte Carlo simulations
UW- Madison Geology 777 Monte Carlo simulations With the development of PCs, Monte Carlo simulations of electron-beam interactions have been very easy to perform. You can input your specific sample composition and run various “what if” scenarios, e.g. what is the maximum penetration of the electron beam through a thin film, or what is the smallest size crystal in a glass matrix that can be analyzed. You will be performing some of these MC simulations in a take home exercise. Each MC run has distinct conditions: specific E0, specific composition (Atomic wt and average Z), density, and potentially different tilt angle.

Monte Carlo simulations: download CASINO for homework assignment
UW- Madison Geology 777 Monte Carlo simulations: download CASINO for homework assignment Go to Download ONLY version 2.51. There are other more recent ones, but more complicated to run; we stick with 2.51 which does everything we need. This is a Windows program. If you have a MAC, you will need either to run it under Bootcamp or use a Windows PC emulator—or run on a Windows computer. We have one in Weeks 306 if you don’t have access otherwise.

UW- Madison Geology 777 Specimen Heating Castaing (1951) derived the maximum temperature rise in a solid impacted by electrons of E0 energy and i current (in mA) and beam diameter d (mm): DT = 4.8 E0 i /kd where k is thermal conductivity (W/cmK). For E0=20 keV and 20 nA, d=1 um, in a metal (k=1), DT is 2 K. In a typical mineral (k=0.1), DT is 20 K. And in organic material, (k=0.002), DT is 1000 K! (e.g. epoxy) Difficult materials: carbonates, hydrated materials, halides, phosphates, glasses, feldspars. (Reed 1993, p 158)

“Harper’s Index” of EPMA
UW- Madison Geology 777 “Harper’s Index” of EPMA 1 nA of beam electrons = 10-9 coulomb/sec 1 electron’s charge = 1.6x coulomb thus, 1 nA = 1010 electrons/sec (10 billion electrons/sec) Probability that an electron will cause an ionization: 1 in 1000 to 1 in 10,000 thus, 1 nA of electrons in one second will yield 106 ionizations/sec Probability that ionization will yield characteristic X-ray (not Auger electron): 1 in 10 to 4 in 10. thus, our 1 nA of electrons in 1 second will yield 105 xrays (in ALL directions). Probability of detection: for EDS, solid angle < 0.01 (1 in 100). WDS, <.001 ergo 103 X-rays/sec detected by EDS, and 102 by WDS. These are for pure elements. For EDS, 10 wt%, 102 X-rays; 1 wt% 10 X-rays; 0.1 wt % 1 X-ray/sec. ergo, counting statistics are very important, and we need to get as high count rates as possible within good operating practices. Acknowledgement: I first encountered this treatment at the Lehigh Microscopy Summer School

UW- Madison Geology 777 Sources of X-ray data Handbook of X-ray Data (Zschornack, 2007) pdf (777 web page) J.A. Bearden, (NBS; AEC) White et al (“Penn State” 1965) tables main lines in tables in Goldstein et al, and Reed texts Probe for EPMA database (includes higher order lines for WDS), also online at <epmalab.uoregon.edu/UCB_EPMA/xray> NIST database: Lawrence Berkeley National Lab online at xdb.lbl.gov for data

Electrons and X-rays … don’t get them confused !
X-rays have no mass, no charge; electrons have charge (key!) and a small mass X-rays can be produced by accelerating HV electrons in a vacuum and colliding them with a target. The resulting electron-generated X-ray spectra contains (1) continuum or continuous background (Bremsstrahlung), (2) occurrence of sharp lines (characteristic X-rays), and (3) a cutoff of continuum at a short wavelength/high keV. X-rays can also generate other x-rays, but unlike the above process, NO Bremsstrahlung is produced!

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