Beam – Specimen Interactions Signals Backscattered Electrons Beam electrons scatter, and escape out of specimen primary signal from elastic scattering Example: Cu target 70% absorbed 30% backscattered Backscattered Electron Coefficient η = # BSE / # incident electrons Backscattered Electrons: Atomic # dependence More trajectories intersect surface with higher Z target Al 1μm η = 14.0% Au – same scale as Al 0.2 μm Au η = 53.5% 0.6 Weak Z contrast Backscatter coefficient η 0.5 0.4 0.3 0.2 Strong Z contrast 0.1 0.0 0 20 40 60 80 Atomic Number η = -0.0254 + 0.016Z – 1.86X10-4Z2 + 8.3X10-7Z3 For multi-component material: η = ∑Ciηi 100 Si target 00 tilt η=17.5 450 tilt η=30.0 Backscattered electrons: Energy distribution BSE have usually undergone a number of scattering events in target prior to emerging Al 0 Pb E0 Light elements = broad distribution most BSEs E << E0 0 E0 Heavy elements = distribution skewed toward E0 Backscattered electrons: Spatial distribution Electrons may emerge from an area outside beam incidence area Al Pb 0 0 2 μm Light elements = broad distribution Heavy elements = narrow distribution Backscattered Electrons Greater energy loss farther from beam (more inelastic scattering events) Better BSE resolution obtainable if select only highest energy BSEs BSEs within 10% of E0 # BSE All BSEs Distance from beam → Beam – Specimen Interactions Signals From Inelastic Scattering • X-Rays Definition: Those electrons emitted with energy less than Continuum 50 eV Characteristic dη/d(E/E0) • Secondary Electrons III I II 0 • Auger Electrons 1.0 E/E0 Produced by interaction of beam and weakly-bound conduction band electrons. E transfer = a few eV Peak emitted ~ 3-4 eV Very shallow sampling depth Intensity of SE • Cathodoluminescence 0.0 2.5 5.0 Depth Z (nm) 7.5 Secondary electron coefficient δ = # SE / # incident beam electrons Dependent on atomic number if λ = mean free path maximum emission depth ~ 5λ For metals: λ ~ 1nm abundant conduction band electrons lots of inelastic scattering of SE Insulators: λ ~ 10 nm Information depth for SE ~ 1/100 of BSE About 1% of primary beam electron range (Kanaya-Okayama range) Secondary electrons generated by primary beam electrons entering (I), or backscattering (II) Can define two SE coefficients: δI and δII SE generation generally more efficient via BSE (δII / δI= 3 to 4) Greater path length in region defined by escape depth, plus increased scattering cross sections due to larger energy distribution (extending to lower energies) in BSEs… primary 5λ BSE Secondary electron density (#SE / unit area) defines apparent resolution Generate SEI within λ / 2 of beam (~0.5nm for metals) Primary beam ~ unscattered in 5λ region Diameter of SEI escape = diameter of beam + 2X λ / 2 SEII occur over entire BSE escape area 1 μm or more – but peak sharply in center SEI SEII distance SEtot Influence of beam energy η+δ E1 E0 incident Shape due mainly to variation in δ E2 Some considerations for resolution… With metal coating, secondary electrons detected primarily from coating In some cases, can improve resolution using higher beam energy (remember – higher kV = higher brightness and smaller beam spot size 10kV 30kV Si target 20nm Au on Si substrate 10kV SE emission volume 30kV Beam – Specimen Interactions Signals From Inelastic Scattering • Secondary Electrons • X-Rays Continuum Characteristic Produced by deceleration of beam electrons • Auger in Electrons coulomb field of target atoms • Cathodoluminescence → energy loss Expressed as emission of X-Ray photon Results in continuous spectrum Most energetic = lowest wavelength Short λ limit = Duane-Hunt limit Results in background spectrum X-ray emission from Cu 7 N x 10-6 photons / e- Ster Cu Lα 5 Cu Kα theoretical 3 Actual – due to sample and window absorption + low detector efficiency Cu Kβ 1 0 2 4 6 Energy (keV) 8 10 X-ray continuum Increase beam energy Max continuum energy increases (short λ limit decreases) Intensity at given energy increases Intensity is a function of Z and photon energy Kramers’ Law I (continuum) ~ ipZ (E0 –Ev)/Ev ip = probe current Z = atomic # E0 = beam energy Ev = continuum photon energy Background intensity is a determining factor in detection limits Beam – Specimen Interactions Signals From Inelastic Scattering • Secondary Electrons • X-Rays Continuum Characteristic INNER SHELL IONIZATION 1) If energy equal or greater than critical excitation potential… Can eject inner shell electron • Auger Electrons Vacuum 2) Atom wants to return to ground state outer shell electron fills vacancy – Valence level relaxation • Cathodoluminescence M… Kα LIII (2p3/2) LII (2p1/2) LI (2s) K (1s) Outer shell electron = higher energy state relative to inner shell electron some energy surplus in the transition → photon emission (X-ray) The emitted X-ray is characteristic of the target element – Wavelength (or energy) = the transition energy Therefore is a manifestation of the electron configuration. Example: E SiKα = E FeKα = 1.740 keV (7.125Å) 6.404 keV (1.936Å) Quantum state of an electron - Quantum numbers Z Polar coordinates… θ Space geometry of the solution of the Schrodinger equation for the hydrogen atom… Y Φ Ψ(r,θ,Φ) = R(r)P(θ)F(Φ) X n l Radial component Principal quantum number Ml Colatitude Orbital quantum number Azimuthal Magnetic quantum number Yields three equations for three spatial variables Quantum state of an electron - Quantum numbers 3 spatial coordinates n l Principal (shell) 1, 2, 3, … radial = size K, L, M… Orbital – angular momentum (subshell) 0 to n-1 ml s (sharp) l=0 p (principal) l=1 d (diffuse) l=2 f (fundamental) l=3 shape so if n = 2, l = 1: 2p Orbital – Orientation (Magnetic, energy shift, or energy level for each subshell) orientation l to – l ex: for l = 2: ml = -2, -1, 0, 1, 2 Rudi Winter Aberystwyth University Quantum state of an electron - Quantum numbers ms Spin ½,-½ Single electron state of motion… n, l, ml, ms or: n, l, j, ml Rudi Winter Aberystwyth University J Total angular momentum (quantum number j ) l +/- ½ = l + ms (except l = 0, where J = ½ only) The Orbitron: Mark Winter, Univ. of Sheffield http://winter.group.shef.ac.uk/orbitron 1s 4f 2p 3d 5f Quantum Numbers for Electrons in Atomic Electron Shells X-ray notation Modern notation n l j=l+s (2j + 1) K 1s 1 0 1/2 2 LI 2s 2 0 1/2 2 LII 2p1/2 2 1 1/2 2 LIII 2p3/2 2 1 3/2 4 MI 3s 3 0 1/2 2 MII 3p1/2 3 1 1/2 2 MIII 3p3/2 3 1 3/2 4 MIV 3d3/2 3 2 3/2 4 MV 3d5/2 3 2 5/2 6 NI 4s 4 0 1/2 2 NII 4p1/2 4 1 1/2 2 NIII 4p3/2 4 1 3/2 4 NIV 4d3/2 4 2 3/2 4 NV 4d5/2 4 2 5/2 6 NVI 4f5/2 4 3 5/2 6 NVII 4f7/2 4 3 7/2 8 Ionization processes - Critical Excitation Potential What voltage is necessary to ionize an atom? Must overcome the electron binding energy – depends on Electron quantum state (shell, subshell, and angular momentum) Atomic # (Z) Electron binding energies (eV) Element K L-I L-II L-III M-I M-II M-III 1s 2s 2p1/2 2p3/2 3s 3p1/2 3p3/2 6 C 284.2* 7 N 409.9* 37.3* 8 0 543.1* 41.6* 11 Na 1070.8+ 63.5+ 30.65 30.81 12 Mg 1303.0+ 88.7 49.78 49.50 13 Al 1559.6 117.8* 72.95 72.55 14 Si 1839 149.7*b 99.82 99.42 15 P 2145.5 189* 136* 135* 16 S 2472 230.9 163.6* 162.5* 26 Fe 7112 844.6+ 719.9+ 706.8+ 91.3+ 52.7+ 52.7+ 29 Cu 8979 1096.7+ 952.3+ 932.7 122.5+ 77.3+ 75.1+ 57 La 38925 6266 5891 5483 1362*b 1209*b 1128*b 82 Pb 88005 15861 15200 13035 3851 3554 3066 92 U 115606 21757 20948 17166 5548 5182 4303 Electron binding energies (eV) Element 2kV beam… K L-I L-II L-III M-I M-II M-III 1s 2s 2p1/2 2p3/2 3s 3p1/2 3p3/2 6 C 284.2* 7 N 409.9* 37.3* 8 0 543.1* 41.6* 11 Na 1070.8+ 63.5+ 30.65 30.81 12 Mg 1303.0+ 88.7 49.78 49.50 13 Al 1559.6 117.8* 72.95 72.55 14 Si 1839 149.7*b 99.82 99.42 15 P 2145.5 189* 136* 135* 16 S 2472 230.9 163.6* 162.5* 26 Fe 7112 844.6+ 719.9+ 706.8+ 91.3+ 52.7+ 52.7+ 29 Cu 8979 1096.7+ 952.3+ 932.7 122.5+ 77.3+ 75.1+ 57 La 38925 6266 5891 5483 1362*b 1209*b 1128*b 82 Pb 88005 15861 15200 13035 3851 3554 3066 92 U 115606 21757 20948 17166 5548 5182 4303 Electron binding energies (eV) Element 15kV beam… K L-I L-II L-III M-I M-II M-III 1s 2s 2p1/2 2p3/2 3s 3p1/2 3p3/2 6 C 284.2* 7 N 409.9* 37.3* 8 0 543.1* 41.6* 11 Na 1070.8+ 63.5+ 30.65 30.81 12 Mg 1303.0+ 88.7 49.78 49.50 13 Al 1559.6 117.8* 72.95 72.55 14 Si 1839 149.7*b 99.82 99.42 15 P 2145.5 189* 136* 135* 16 S 2472 230.9 163.6* 162.5* 26 Fe 7112 844.6+ 719.9+ 706.8+ 91.3+ 52.7+ 52.7+ 29 Cu 8979 1096.7+ 952.3+ 932.7 122.5+ 77.3+ 75.1+ 57 La 38925 6266 5891 5483 1362*b 1209*b 1128*b 82 Pb 88005 15861 15200 13035 3851 3554 3066 92 U 115606 21757 20948 17166 5548 5182 4303 Electron binding energies (eV) Element 20kV beam… K L-I L-II L-III M-I M-II M-III 1s 2s 2p1/2 2p3/2 3s 3p1/2 3p3/2 6 C 284.2* 7 N 409.9* 37.3* 8 0 543.1* 41.6* 11 Na 1070.8+ 63.5+ 30.65 30.81 12 Mg 1303.0+ 88.7 49.78 49.50 13 Al 1559.6 117.8* 72.95 72.55 14 Si 1839 149.7*b 99.82 99.42 15 P 2145.5 189* 136* 135* 16 S 2472 230.9 163.6* 162.5* 26 Fe 7112 844.6+ 719.9+ 706.8+ 91.3+ 52.7+ 52.7+ 29 Cu 8979 1096.7+ 952.3+ 932.7 122.5+ 77.3+ 75.1+ 57 La 38925 6266 5891 5483 1362*b 1209*b 1128*b 82 Pb 88005 15861 15200 13035 3851 3554 3066 92 U 115606 21757 20948 17166 5548 5182 4303 Electron binding energies (eV) Element 50kV beam… K L-I L-II L-III M-I M-II M-III 1s 2s 2p1/2 2p3/2 3s 3p1/2 3p3/2 6 C 284.2* 7 N 409.9* 37.3* 8 0 543.1* 41.6* 11 Na 1070.8+ 63.5+ 30.65 30.81 12 Mg 1303.0+ 88.7 49.78 49.50 13 Al 1559.6 117.8* 72.95 72.55 14 Si 1839 149.7*b 99.82 99.42 15 P 2145.5 189* 136* 135* 16 S 2472 230.9 163.6* 162.5* 26 Fe 7112 844.6+ 719.9+ 706.8+ 91.3+ 52.7+ 52.7+ 29 Cu 8979 1096.7+ 952.3+ 932.7 122.5+ 77.3+ 75.1+ 57 La 38925 6266 5891 5483 1362*b 1209*b 1128*b 82 Pb 88005 15861 15200 13035 3851 3554 3066 92 U 115606 21757 20948 17166 5548 5182 4303 Kα ψp1 ψp ψp2 ψ1s Kβ ψp1 ψp ψp2 ψ1s Energy (or wavelength) of an X-ray depends on Which shell ionization took place Which shell relaxation electron comes from K radiation Electron removed from K shell Kα electron fills K hole from L shell Kβ electron fills K hole from M shell L radiation Electron removed from L shell Lα electron fills L hole from M shell Lβ electron fills L hole from M or N shell Karl Manne Siegbahn depends on which b transition – which L level ionized and which M or N level is the source of the de-excitation electron Energy level representation of characteristic X-ray emission process Vacuum Valence level M… Kα LIII (2p3/2) LII (2p1/2) LI (2s) Sufficiently energetic beam electron ionizes K shell… K (1s) L1 (2s) → K (1s) , why not? Selection rules for allowed transitions involving photon emission (conservation of angular momentum) Change in n (principal) must be ≥ 1 Change in l (subshell) can only be +1 or -1 Change in j (total angular momentum) can only be +1, -1, or 0 The photon, following Bose-Einstein statistics, has an intrinsic angular momentum (spin) of 1. So a K-shell vacancy must be filled by an electron from a p-orbital, but can be 2p (L), 3p (M), or 4p (N) So can’t fill K from L1 (2s) in transitions involving photon emission X-Ray lines and electron transitions Normal (diagram) level Energy level (core or valence) described by removal of single electron from ground state configuration Diagram lines Originate from allowed transitions between diagram levels Non-diagram (Satellite) lines Generally originate from multiply-ionized states Two vacancies of one shell (e.g. two K ionizations) → hypersatellite Other effects from: Auger effect, Coster-Kronig (subshell) transitions, etc. Originally Ionized shell Filled from… Energy of Kα X-Ray Bohr’s Three Postulates: 1) There are certain orbits in which the electron is stable and does not radiate The energy of an electron in an orbit can be calculated - that energy is directly proportional to the distance from the nucleus Bohr simply forbids electrons from occupying just any orbit around the nucleus such that they can’t lose energy and spiral in… 2) When an electron falls from an outer orbit to an inner orbit, it loses energy …expressed as a quantum of electromagnetic radiation 3) A relationship exists between the mass, velocity and distance from the nucleus of an electron and Planck’s quantum constant… From these principles, Bohr realized he could calculate the energy corresponding to an orbit: m = mass of electron e = charge of electron Δ§ = h / 2π If an electron jumps from orbit n=2 to orbit n, the energy loss is: energy is radiated, and expressing Plank’s relationship in terms of angular frequency (ω), rather than frequency (ν): Bohr theoretically has expressed Balmer’s formula and could calculate the Rydberg constant knowing m, e, c, and Δ§ Balmer and Paschen series in terms of frequency (n and m are integers)… Multply both sides by Plank’s constant, h …Bohr assumes this is equal to the energy difference between two stationary states…. Single set of energy values to account for E differences… And binding energy… Electron bound to + nucleus n identifies a stationary state Bohr assumes that proton and electron orbit around center of mass to derive orbital frequency of electron, then, arrives at an expression for radiation frequency for electron cascading through stationary states… From expression of binding energy, and orbital frequency of electron, and solving for R in terms of physical constants… For large n m = mass of electron e = charge ε= permittivity constant From Coulomb’s Law Substituting the expression for R into expression for binding energy, gives binding energies of stationary states (Z is atomic #) Now, an electron making K transition moves in field of force – potential energy function: Seeing the charge of the nucleus (Z-1)e, and the other n=1 electron. And from the equation above for binding energy, the transition energy is… An approximate expression for the energy of the Kα X-Ray (Bohr’s early quantum theory) Or about (10.2 eV)(Z-1)2 So: O = 0.5 keV Si = 1.7 keV Ca = 3.7 keV Fe = 6.4 keV Moseley’s Law Niels Bohr X-Ray energy is related to Z… empirical relationship E = A(Z-C)2 (A and C are constants) Bohr theory prediction for Kα … Kα Kβ Henry Moseley E = (10.2)(Z-1)2 Produce overall X-ray spectrum Characteristic peaks superimposed on a continuum background X-rays can be detected and displayed discriminated either by energy (E) or wavelength (λ) Energy Dispersive Spectrometry (EDS) Background Complex spectrum from monazite (Ce, La, Nd, Th) PO4 For heavy elements Complex spectra → peak overlaps Note low pk / bkg for Th Wavelength Dispersive Spectrometry (WDS) SiKα Si in garnet (pyrope) TAP monochromator CaKα (2nd order) SiKβ For heavy elements Complex spectra → peak overlaps Note low pk / bkg for Th Monazite (LIF monochromator) in wavelength region of NdL EDS spectrum Depth of production of X-Rays X-Rays generated over much of the interaction volume Characteristic X-Rays produced in electron range where electron energy exceeds critical excitation potential Z dependent Recall ionization energies (keV)… K Si 1.55 Ca 4.03 Fe 7.10 Sn 29.1 Pt L M 4.46 13.9 3.3 X-Ray region will be dependant on both Z and density (ρ) Φ(ρZ) High density = limited depth of production Deeper production for low energy ionizations X-Ray spatial resolution 3 g/cm3 20 keV 10 g/cm3 Run PHIROZ95, Casino, Win X-Ray Compare effects of different beam energies different materials Different lines generated in different regions of interaction volume Depends on electron energy distribution so function of: Initial voltage Material properties (Z, ρ) Critical excitation potentials for ionization events of interest 75% 50% 25% 10% 5% Energy contours Electron energy 100% Labradorite [.3-.5 (NaAlSi3O8) – .7-.5 (CaAl2Si2O8), Z = 11] 15 kV 1% 10 kV 50% 1 mm 5 kV 25% (~ Ca K ionization energy) 10% 5% 5% 1 kV (~ Na K ionization energy) 10% 25% 50% 75% 100% Labradorite [.3-.5 (NaAlSi3O8) – .7-.5 (CaAl2Si2O8), Z = 11] 15 kV Three main conclusions: For same material: line M L K generation volume large medium small K line of heavy element is excited from smaller region than K line of light element K line of an element is excited from smaller volumes in denser, or higher average Z materials Putting it together… Pb, Th, and U in monazite Ionization energy for PbM-V level (to generate PbMα) = 2.484 keV Ionization energy for ThM-V level = 3.332 keV Ionization energy for UM-IV level (to generate UMβ) = 3.728 keV will be trace element so ~ double the overvoltage to get reasonable count rates = 8 keV (minimum beam energy) 2.484 keV ionization potential… This is the lowest required energy of the three elements (Pb, Th, U) and will, therefore, limit the analytical resolution beam voltage 5 10 15 20 25 30 % of beam voltage 49.68 24.84 16.56 12.42 9.936 8.28 5 keV (2.484 keV ionization potential for Pb M-V level is ~50% of the beam energy) Monte Carlo simulation Electron paths Energy contours 50%~ 40nm 15 keV (2.484 keV ionization potential for Pb M-V level is ~17% of the beam energy) Monte Carlo simulation Electron paths Energy contours 17% ~480nm 2,500 Analysis resolution in monazite Depth of PbM-V ionization (nm) 2,000 1,500 1,000 500 0 0 5 10 15 20 Accelerating voltage (keV) 25 30 35 800 Analysis resolution in monazite 700 Remember, voltage limited to minimum of 8 kV (2x ionization energy of UM-IV) Depth of PbM-V ionization (nm) 600 500 Spatial resolution limit is then ~120 nm 400 300 200 100 0 0 2 4 6 8 10 Accelerating voltage (keV) 12 14 Analytical spatial resolution: DAR = (Dbeam2 + Dscattering2)1/2 Dbeam = beam diameter Dscattering = scattering dimension, either depth or radial distribution defined by xray emission volumes Based on depth containing 99.5% of total emitted intensity Based on radius containing 99.5% of intensity 2000 φ(ρZ) Analytical Resolution PbMα in Monazite AR Pb Mα (nm) 1500 D Beam (nm) 1000 800 600 500 400 300 50 10 0 0 AR Pb Mα (nm) 2000 10 E0 keV 20 30 20 30 Radial Analytical Resolution PbMα in Monazite 1500 D Beam (nm) 1000 800 600 500 400 300 50 10 0 0 10 E0 keV 500 Beam diameter 400 nm AR Pb Mα (nm) 400 300 nm 300 200 nm 200 Analytical Resolution PbMα in Monazite 100 nm Radial φ(ρZ) 50 nm 10 nm 100 4 5 6 7 8 E0 keV 9 10 11 The ionization range can be estimated by means of a simple relationship 33 ∗ π΄ π ππ = πΈ01.7 − πΈπ 1.7 π∗π Castaing (1952); Merlet and Llovet (2013) where E0 and Ec are expressed in keV, A is the atomic weight (g/mol), Z is atomic number, and ρ is density (g/cm3). π·πππ πππ’π‘πππ (ππ) = π 2 + π΅2 Where R is the ionization range (in nm), and B is the beam diameter (in nm) Other signals from inelastic scattering Auger process Core level ionization De-excitation via internal conversion and emission of another electron rather than X-Ray → doubly ionized state Can result in satellite X-ray emission (Characteristic of electron configuration) e- (KLILIII) Vacuum X-ray emission Ka2 Vacuum Auger process Valence level Valence level M… M… LIII (2p3/2) LII (2p1/2) LI (2s) LIII (2p3/2) LII (2p1/2) LI (2s) K (1s) K (1s) Very small perturbation on background of emitted electrons - Very low yield Low energy - emitted from surface ~ 0.1nm depth (surface analysis technique) Auger spectroscopy Sample upper 20Å or so and evaluate kinetic energy of emitted electrons. Materials Evaluation and Engineering, Inc. http://mee-inc.com/ Cathodoluminescence Some insulators and semiconductors emit photons in the visible and UV when exposed to the electron beam ~ empty conduction band ~ full valence band The band gap has characteristic energy 1) Promote electron to conduction band Electron – hole pair 2) Recombination 3) Excess energy = band gap energy Expressed as photon (visible) Cathodoluminescence Emitted photon energy = full band gap energy Emitted photon energy = impurity donor level ν = E(gap) / h ν = E(gap-d) / h Conduction band Almost Empty Eg bandgap donor level Valence band Almost Full Initial state 1. Inelastic scattering imparts energy to specimen. Electron promoted to conduction band. 2. Recombination of electron-hole pair results in photon emission Electron promoted from impurity donor level 100 mm Sandstone, secondary electron image 100 mm Panchromatic CL image. Bright = K-fsp, dark = quartz. 40x60 micron 560nm CL image of diatoms 2.0-1.95 eV. Non-bridging hole centers 2.15eV. Self-trapped excitons related to Si nanoclusters? 16x12 micron 560nm CL image of diatoms Butcher et al. (2003) Photoluminescence and Cathodoluminescence Studies of Diatoms – Nature’s Own NanoPorous Silica Structures Integration of WDS and cathodoluminescence mapping. InGaN epilayers. In:Ga ratio 0.13 40000 428nm 0.11 4000 418nm CL counts Peak CL wavelength Edwards et al. (2003) Simultaneous composition mapping and hyperspectral cathodoluminescence imaging of InGaN epilayers Cathodoluminescence spectrum Shifts energies and / or intensities due to impurities or crystal dislocations and other defects thin bulk Thin with lattice defects Spectrum from GaAlAs