6. Analytical Electron Microscopy

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1 Physical Principles of Electron Microscopy 6. Analytical Electron Microscopy Ray Egerton University of Alberta and National Institute of Nanotechnology Edmonton, Canada

2 The aim of analytical electron microscopy (AEM) TEM and SEM imaging à physical structure of the specimen. Analytical electron microscopy à elemental ( chemical ) structure BSE imaging in SEM, HAADF imaging in STEM are Z-dependent but we need a more precise Z-specific signal to distinguish between all elements in the Periodic Table. Inner electron shells of atoms have energies that can be measured by spectroscopy and which are highly element-specific. Either x-ray or electron spectroscopy can be used.

3 Bohr model of the atom electron orbits and shells energy levels

4 Bohr model for a hydrogenic atom of atomic number Z Neglecting screening and interaction with other electrons, K(Ze)(e)/r 2 = mv 2 /r, K = 1/(4πε 0 ) electrostatic = centripetal force (mv) r = n (h/2π) quantization of angular momentum h = Js = Planck constant, n = principal quantum number r n = n 2 (h/2π) 2 /(KmZe 2 ) = n 2 a 0 / Z, a 0 = 1 st Bohr radius E n = mv 2 /2 K(Ze)(e)/r n = KZe 2 /(2r n ) K Ze 2 /r n = K Z e 2 /(2r n ) = R (Z 2 /n 2 ) R = 13.6 ev = (first) ionization energy energy of hydrogen

5 Bohr model versus measured K-shell ionization energies

6 Real atoms A more realistic physical model of the atom uses wave mechanics, treating the atomic electrons as de Broglie waves. Analysis then involves solving the Schrödinger wave equation to determine the electron wavefunctions, represented by orbitals (pictured as charge-density clouds) that replace the concept of particle orbits. An exact solution is possible for hydrogen and results in binding energies that are identical to those predicted by Bohr. Approximate methods are used for other Z, and in most cases the calculated energy levels are close to those determined from optical spectroscopy (which involves transitions between levels). Other wave-mechanical principles determine the maximum number of electrons in each atomic shell: 2 for the K-shell, 8 for the L-shell, 18 for the M-shell etc. Because an atom in its ground state represents the minimum-energy configuration, electrons fill these shells in sequence (with increasing Z), starting with the K-shell. The measured energy levels differ substantially between different elements, giving photon energies (energy-level differences) that can be used to identify each element. Except for H and He, these photon energies are above 50 ev and lie within the x-ray region of the electromagnetic spectrum.

7 X-ray Emission Spectroscopy When a primary electron enters a TEM or SEM specimen, it is sometimes scattered inelastically by an inner-shell (e.g. K-shell) electron, causing the latter to undergo a transition to a higher-energy state, leaving the atom with an electron vacancy (hole) in its inner shell. However, the scattering atom remains in this excited state for only briefly: within about s, another atomic electron fills the inner-shell vacancy by making a downward transition from a higher energy level. In this de-excitation process, energy can be released in the form of a characteristic x-ray photon whose energy (hf ) is given by the difference in binding energy between the upper (n u ) and lower (n l ) levels. n u K-emission implies n l = 1, L implies n l = 2, M implies n l = 3 etc. A Greek subscript represents the change in quantum number: α means (n u n l ) = 1, β means (n u n l ) = 2, γ means (n u n l ) = 3. n l

8 X-ray emission spectrum X-ray emission spectrum (number of x-ray photons as a function of photon energy) recorded from a TEM specimen (NiO thin film on a Mo grid), showing characteristic peaks due to the elements C, O, Ni, Mo, and Fe. For Ni and Mo, both K- and L-peaks are visible.

9 Bremstrahlung background The characteristic peaks in the x-ray emission spectrum are superimposed on a continuous background that arises from the bremsstrahlung process (Bremstrahlen = braking radiation, implying deceleration of the electron). If a primary electron passes close to an atomic nucleus, it is elastically scattered and follows a curved path. During its deflection, the electron experiences a Coulomb force and a resulting centripetal acceleration toward the nucleus. Being a charged particle, it must emit electromagnetic radiation, with an amount of energy that depends on the impact parameter of the electron. Impact parameter is a continuous variable, slightly different for each primary electron, so the photons emitted have a broad range of energy and form a continuous background to the characteristic peaks in the x-ray emission spectrum.

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11 X-ray Energy-Dispersive Spectroscopy (XEDS) In x-ray energy-dispersive (EDX) spectroscopy, the dispersive device is a semiconductor diode, fabricated from a single crystal of silicon and similar to the BSE detector in an SEM. If an x-ray photon enters and penetrates to the transition region (between p- and n-doped material), it can release a considerable number of outer-shell (valence) electrons from a particular atom. This process is equivalent to exciting electrons from the valence to the conduction band (creation of electron-hole pairs) and results in electrical conduction by both electrons and holes for a brief period of time. With a reverse-bias voltage applied to the diode, this conduction causes a charge to flow, proportional to the number N of electron-hole pairs generated. If all of the photon energy (h f ) goes into creating electron-hole (e-h) pairs, each pair requiring an average energy ΔE, energy conservation implies: N = h f / ΔE For silicon, ΔE 4 ev (> energy gap between valence and conduction bands), therefore a Cu-Kα photon creates about (8000eV)/(4eV) = 2000 e-h pairs.

12 Si(Li) EDX detector (schematic) and its signal-processing circuitry

13 EDX pulse processing and display pulse-height analysis (PHA) multichannel analyser (MCA) Voltage output signals of (a) the FET preamplifer, (b) the pulse-processor circuit, (c) the analog-to-digital converter (ADC), giving (d) the spectrum display.

14 Count-rate limitation PHA requires a conversion time to analyze the height of each pulse. X-ray photons arrive at random and if another x-ray photon arrives within this conversion time a false reading would occur, so the PHA circuit ignores such double leading to dead time which increases as photon-arrival rate increases. The beam current in the TEM or SEM should be kept low enough to ensure that the dead time is less than about 50%, otherwise the number of photons measured in a given recording time starts to fall.

15 Silicon drift detector (SDD) has largely replaced the Si(Li) detector because count rate can be higher, thermoelectric cooling (instead of liq. N 2 ) is sufficient, and the design allows large-area detectors.

16 Dead time versus input count rate Courtesy of N.J. Zaluzec, M&M meeting 2003

17 Si(Li) and SDD EDX-spectrometers Si(Li) detector with its liquid-nitrogen reservoir Large-area SDD system (with liq. N 2 cooling) installed in an fei TEM

18 Requirements for quantitative spectroscopy Characteristic X-rays are emitted isotropically (over 4π steradians) Collection solid angle = (detector area)/(distance from sample) ~ 0.1 steradian with Si(Li) detector ~ 1 steradian for large-area SDD detector Especially in the TEM, where high spatial resolution is often the aim, the beam current is low (e.g. < 1 na for a 1nm-diameter probe). So the x-ray count rate may be low. Poisson statistics: if a characteristic peak contains N counts, the variance is N and standard deviation is N 1/2 (shot noise).. Signal/noise ratio: SNR = N/N 1/2 = N 1/2 = 0.1 (10% accuracy) if N = 100.

19 EDX peak width and artifacts Peak FWHM: eV determined by e-h statistics. System peaks minimized by: Be tip to TEM specimen holder No TEM objective aperture Thick condenser apertures Test specimen: NiO thin film on a Mo grid. Mo peaks come from the grid + stray radiation outside the probe (hole count). Fe peak is from TEM polepieces.

20 Quantitative x-ray analysis in the TEM The number N A of x-ray photons in a characteristic peak depends on: * elemental concentration n A (atoms of element A per unit volume) ß needed * specimen thickness t (proportional to t for a thin specimen) * number N e of electrons passing through the sample during recording time, * ionization cross section σ A for creating a hole in an inner shell of element A. (this cross section can be interpreted as a target area for inelastic scattering; the value of σ A depends on Z and the type of inner shell: K, L, etc.) fluorescence yield ω A (not every inner-shell vacancy gives x-ray emission, the release of Auger electrons may occur instead). collection efficiency η, dependent on the solid angle of the x-ray detector so that N A = (n A t) σ A ω A η N e where n A t = areal density (atoms/area) n A /n B = [(σ B ω B )/(σ A ω A )] (N A /N B ) = k AB (N A /N B ) ß k-factor method

21 Quantitative x-ray analysis in the SEM Electrons penetrate until they are absorbed in the specimen. X-rays are created within the interaction volume but may be absorbed (photoelectric effect), depending on creation depth and absorption coefficient. This coefficient depends on chemical composition, which is unknown. But can first ignore x-ray absorption and get first estimate of composition, then correct for absorption, giving a better estimate of composition, etc. Another complication is x-ray fluorescence, which can be calculated if the composition is known, so the ZAF procedure includes this in the iteration. The electron microprobe is similar to the SEM but is optimised for high beam current rather than high resolution (limited for the x-ray signal by beam spread). It is capable of < 10-4 composition accuracy (on a flat specimen) using ZAF and normallyuses a wavelength-dispersive x-ray (WDX) spectrometer, which is based on x-ray diffraction and gives superior (~ 1eV) energy resolution so that background subtraction to characteristic peaks can be more precise.

22 Wavelength-dispersive x-ray instruments SEM + WDX spectrometer AEI EMMA-4 WDX-TEM modern EPMA (Jeol)

23 X-ray wavelength-dispersive spectroscopy (XWDS) Bragg law for x-rays: n λ = 2 d sin θ i θ i is changed by moving the analysing crystal and the x-ray detector (twice as fast) around the Rowland circle. To cover the wavelength range λ = 0.1nm to 1nm, several crystals (e.g. LiF, quartz, mica, organic) are used. Collection efficiency is low but high beam current compensates for this. θ i

24 WDX spectra Narrow peaks (less overlap), low background, Z down to 3 (Li) Left: WDX spectrum of MoS 2 showing Mo L-peaks and S K-peaks. Right: EDX spectrum, where Mo and S peaks overlap and are not resolved.

25 Auger spectroscopy Even though XWDS makes light elements detectable, the sensitivity is reduced because the de-excitation process for low-z elements involves mainly Auger emission. In Auger spectroscopy, these electrons are analysed in an electron spectrometer and their characteristic energies permit elemental analysis. However, these energies are typically a few hundred ev and these electrons are strongly scattered and absorbed in a solid, as they have a shallow (~2nm) escape depth. This requires ultrahigh vacuum (UHV) and in-situ surface preparation otherwise the spectrometer sees only the hydrocarbon contamination layer on a technical (air-exposed) surface. This possible in special surface-science equipment (e.g. Auger microscope) but not in a typical TEM or SEM. E Auger emission

26 Mean free path λ i for inelastic scattering as a function of incident-electron energy (above the Fermi level) The solid curve represents a least-squares fit to experimental data from many inorganic materials

27 Electron energy-loss spectroscopy (EELS) For every emitted x-ray or Auger electron, an inner-shell vacancy must be created by inelastic scattering of a primary electron. We can measure this scattering by putting an electron spectrometer in the path of the electrons transmitted through a thin specimen, to form an electron energy-loss spectrum. The energy losses are characteristic of the specimen. Inner-shell scattering gives an ionization edge at the binding (ionization) energy of each atomic shell. Identification of these edges indicates the elements present in the thin specimen. Their integrated intensity is a measure of the concentration of each element. n A / n B = (I A / I B ) (σ B /σ A ) Similar to the k-factor method of EDX analysis except that the cross sections (σ B and σ A ) can be calculated. Fluorescence yield does not matter since number of energy-loss electrons = number of x-ray photons + number of Auger electrons. Scattering by outer-shell (valence or conduction) electrons gives a plasmon peak with an energy loss (5 ev 30 ev) that depends on the electron density because the scattering causes a plasma oscillation of frequency f, equivalent to creating a photon of energy hf.

28 Electron energy-loss spectrum of YBCO superconductor showing Ba M- and N-edges, oxygen K-edge and weak ionization edges from copper and yttrium. The plasmon peak represents inelastic scattering from valence electrons. Courtesy of D.H. Shin (Ph.D. thesis, Cornell University).

29 Electron energy-loss spectrometer A high-resolution spectrometer is desirable, to give a resolution < 10-5 ~ 1eV. For a magnetic induction B perpendicular to the incoming electrons (speed v) evb = F = mv 2 /R giving circular path of radius R = mv/eb that depends on the energy loss E of the electron due to inelastic scattering in the specimen.

30 Electron energy-loss spectrometer below a TEM column Advantages of EELS: energy resolution better than 1eV (can give bonding information), allows high spatial resolution Disadvantages: very thin specimen, more difficult technique