Introduction to Electron Microscopy-II Prof. David Muller, dm24@cornell.edu Rm 274 Clark Hall, 255-4065 Ernst Ruska and Max Knoll built the first electron microscope in 1931 (Nobel Prize to Ruska in 1986) T4 Bacteriophage Electron Microscopy bridges the 1 nm 1 μm gap between x-ray diffraction and optical microscopy
Lenses in a Transmission Microscope (and deflection coils to correct their alignment) Gun: electron source If misaligned, low intensity & other alignments may also be out Condensor: uniformly illuminate the sample If misaligned, you will lose the beam when changing magnification Objective: image sample determines resolution. If misaligned, the image will be distorted, blurry. projector: magnifies image/ forms diffraction pattern should not alter resolution. If misaligned, the image will be distorted, diffraction pattern may be blurry. http://www.rodenburg.org/rodenburg.pdf
Reciprocity Reciprocity: Electron intensities and ray paths in the microscope remain the same if (i) the direction of rays is reversed, and (ii) the source and detector are interchanged. Proof follows from time-reversal symmetry of the electron trajectories and elastic scattering (to all orders). Reciprocity does not hold for inelastic scattering: Sample is after probe forming optics in STEM - energy losses in sample do not cause chromatic blurring in the image Sample is before the imaging optics in TEM energy losses in the sample do cause chromatic blurring in the image. Imaging thick samples in TEM can be improved by energy filtering (so on the zero-loss image is recorded). This is not needed for STEM. From L. Reimer, Transmission Electron Microscopy
Reciprocity TEM STEM Condensor aperture Controls coherence Objective aperture (after sample) Collector aperture Condensor aperture (before sample) Controls resolution Image recorded In parallel Image recorded serially by scanning the source From L. Reimer, Transmission Electron Microscopy
CTEM Gun Reciprocity (or STEM vs. CTEM) Reciprocity STEM Detectors Illumination angle α Collector angle Specimen Objective Aperture Viewing Screen β Specimen Objective Aperture Gun Reciprocity (for zero-loss images): A hollow-cone image in CTEM an annular-dark field image in STEM. However: In STEM, energy losses in the sample do not contribute to chromatic aberrations (Strong advantage for STEM in thick specimens)
Scanning Transmission Electron Microscopy 200 kv Incident Electron Beam (ΔE=1 ev) 1 atom wide (0.2 nm) beam is scanned across the sample to form a 2-D image ADF Signal Er M 4 Edge x y 3 Å Elastic Scattering ~ "Z contrast" 0 0.5 1 1. Distance (nm) Annular Dark Field (ADF) detector Electron Energy Loss Spectrometer Increasing energy loss Single atom David Sensitivity: Muller 2008 P. Voyles, D. Muller, J. Grazul, P. Citrin, H. Gossmann, Nature 416 826 (2002) U. Kaiser, D. Muller, J. Grazul, M. Kawasaki, Nature Materials, 1 102 (2002)
Brightness: Not how many electrons, but how many electrons go where we want them to 10 μm 0.1 μm Electric Field Lines Thermionic Sources: Large Source Weak Electric Field Electrons are boiled off in all directions Low brightness Field Emission Guns: Small Source Strong Electric Field Electrons tunnel out along field lines High brightness
The Brightness Equation Brightness is the current density (J=ΔI/ΔS) per solid angle (ΔΩ=πα 2 ) where α is the half angle E α p n p t ΔI J β = = -(1) 2 ΔS ΔΩ πα For a thermal source, the electron current has a maxwellian momentum distribution. Transverse momentum Normal to the Field Root mean square angle subtended: hence 2 2 p t = 2mkT p n = 2mkT + 2meV 2 α 2 2 = pt pn = 1 1+ β J ev J ev = + π 1 kt π kt Since ev>>kt ( ev kt ) Brightness increase with beam voltage, decrease with tip temperature
Brightness as a limit to Spatial Resolution For current density J and probe diameter d 0, the probe current is ( d ) J 2 I p π 0 2 = -(2) From the Brightness equation (1) we also know J 2 = βπα Hence the probe current depends on π 4 Rearranging, we find the probe size 2 2 2 I p = βd0α -(3) I p 4 0 2 π β = 1 2 1 α d -(4) A small spot size implies a small beam current or large illumination angle
Properties of Electron Sources Tungsten Thermionic LaB 6 Thermionic ZrO 2 /W Schottky FEG W Cold FEG Source Size at 10 pa, 100 kev ~6 nm ~ 2 nm ~0.1 nm ~0.03 nm Brightness at 100 kv (A/cm 2 /Sr) 5 x 10 5 5 x 10 6 10 8 10 9 Energy Spread FWHM (ev) 2 2 0.5 0.3 Operating Temp (K) 2500-3000 1400-2000 1400-1800 300 Lifetime 25-100 hrs 150-300 hrs 3-5 years >5 years Vacuum (Torr) 10-4 -10-5 10-5 -10-6 10-8 -10-9 10-10 -10-11
Tungsten Filament Cheap (~$20) Short lifetime Low brightness Works in poor vacuum
Thermionic LaB 6 Filament ~$1000 Longer life, but can be damaged by thermal shock Medium brightness Needs moderate vacuum http://www.kimphys.com/cathode/catalog_pdf/lab6_cathode_es423.pdf
Schottky Tip design Tip Zr reservoir Expensive (~$20,000?) Long lifetime (years) High brightness Needs good vacuum Tungsten wire filament
Electron Scattering Incident electron Valence electrons can be excited (detected as secondary electrons) Elastic scattering (large angle, α Z 2 ) Inelastic scattering (small angle, α Z) Elastic scattering can only change the direction of the electron, Only inelastic scattering can slow it down (by losing energy in the sample)
Beam Spreading E 0 =200 kev E 0 =20 kev Electron Range (in μm): R 0.064 ρ E 1.5 0 (density ρ in g/cm 3, E 0 in kev) 1 μm of Carbon R~ 100 μm at 200 kev David Joy s simulation code is available at http://web.utk.edu/~srcutk/htm/simulati.htm A more detailed simulator can be found at http://www.gel.usherbrooke.ca/casino/what.html
Beam Spreading For thin films: 2 1.5 200 kev Electrons in Silicon FWHM of feature 90% beam radius b 90% = 625 E 0 ρ A Z t 1.5 Resolution (μm) 1 0.5 0 0 1 2 3 4 5 6 Si thickness (μm) E 0 in kv t in cm, ρ in g/cm 2 A in g/mol At 100 kv: 0.16 nm for 10 nm thick C 1.8 nm for 50 nm thick C
Imaging Buried Atoms (Sb in Si) Sb source turned on here 1 nm No Sb in substrate P. David Voyles, Muller D. 2008 Muller, J. Grazul, P. Citrin, H. Gossmann, Nature 416 826 (2002) number of atomic columns 160 140 120 100 80 60 40 20 0 Null test: No Sb in substrate 0.8 Si columns Si/Sb columns singly-occupied doubly-occupied 0.9 1.0 1.1 1.2 1.3 normalized intensity 1.4
Effect of defocus and aperture size on an ADF-STEM image (200 kv, C 3 =1.2 mm) CTF PSF
What happens with a too-large aperture? ADF of [110] Si at 13 mr, C3=1mm Strong {111} fringes Strong {311} fringes 2 clicks overfocus Best 111 and 311 fringes occur at different focus settings If the aperture is too large
Aperture Size is Critical (200 kv C 3 =1mm) CTF 1 0.8 0.6 0.4 0.2 {220} Si 13 mrad 10 mrad 0 0 0.2 0.4 0.6 0.8 {111} Si k (1/A) 30% increase in aperture size ~50% decrease in contrast for Si {111} fringes
Aperture Size is Critical (200 kv C 3 =1mm) Beam Current Enclosed (pa) 30 25 20 15 10 5 r 80% = 0.25 nm r 64% = 0.1 nm r 80% = 0.8 nm 10 mrad 13 mrad 0 0 0.2 0.4 0.6 0.8 1 Radius (nm) All the extra probe current falls into the tails of the probe reduces SNR
Finding the Aperture with the smallest probe tails (Kirkland, Fig 3.11) 1 ( ) 2 Δf = 0 λ min. 8 C S α opt = 1.22 λ C3 1/ 4
Summary Contrast Transfer Functions: Coherent: α opt 6λ = C 3 1/ 4 d = 0 C λ min. 77 1/ 4 3 3/ 4 Lower resolution, higher contrast Easy to get contrast reversals with defocus Aperture size only affects cutoff in CTF Incoherent: α opt 4λ = C 3 1/ 4 d = 0 C λ min. 43 Higher resolution, lower contrast Harder to get contrast reversals with defocus Aperture size is critical affects CTF at all frequencies 1/ 4 3 3/ 4
3D Tomography of Nanostructures? (Biologists have been doing this for 30 years with TEM) 3D: 1 nm resolution 2D: 0.4 nm Low dose imaging of individual particles Don t need crystals! Herpes simplex Kirrmoycin stalled ribosome at 13Å J. Harms et al., Structure Fold Des 7, 931-41. (1999) Z.H. Zhou et al, J. Mol. Bio.
Tomography in Materials Science (Examples from researchers in my group) Si nanocrystals in SiO 2 Au clusters on Carbon Nanotubes Ta/TaN liner around a copper interconnect M. David Weyland, Muller 2008 A. Yurtserver, P. Ercius, J. Cha 2005
Materials Microscopy Resources on Campus (http://www.ccmr.cornell.edu/facilities/) Type Atomic Force Microscopy Applications Topographic Imaging on wafers Accurate height measurements on flat surfaces (~ 0.5 nm vertical) Lateral Resolution 10-20 nm In-situ no vacuum required Location Dr. Jonathan Shu D-22 Clark Hall Prof. Kit Umbach SB-60C Bard Hall CNF Clean Room Scanning Electron Microscopy Transmission Electron Microscopy Imaging of complex structures at 1-20 nm resolution X-ray mapping at 100-500 nm In-vacuum Clark: High spatial resolution Snee/Bard: best x-ray mapping, OIM 1 nm (polymers) > atomic resolution of crystals in thin samples X-ray mapping at 1 nm EELS at < 1 nm Requires sample thinning (except for nanoparticles) Clark: Mick Thomas F3 Clark Hall Bard/Snee: John Hunt SB56 Bard/1149 Snee Duffield: John Grazul 150 Duffield (TEM+STEM) Clark: Mick Thomas F3 Clark (STEM+EDX)