Introduction to Electron Microscopy

Transcription

1 Introduction to Electron Microscopy Prof. David Muller, Rm 274 Clark Hall, 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

2 Tools of the Trade AFM MFM Scanned Probe Microscope (includes Atomic Force Microscope) Transmission Electron Microscope Scanning Electron Microscope

3 Biological and Electronic Component Dimensions Biological Electronic Components Tool 1 Logic Board 10-2 Computer chip SEM Size (m) Mammalian cell Bacterial cell Optical Microscope TEM Virus Gene Protein Transistor Gate Oxide Atom AFM/STM

4 Comparison of Optical and Electron Microscopes Electron microscopes are operated in vacuum because the mean free path of electrons is air is short this mean biological samples should not degas they can either be dehydrated or frozen pathology, not in-vivo. Electron microscopes have higher resolution than optical microscopes atomic resolution is possible. Chemical imaging and spectroscopy mapping π and σ bonds at 1nm resolution can be done. Radiation damage is severe and limits the image quality and resolution (not as bad as x-rays or neutrons though! see R. Henderson, Quarterly Reviews of Biophysics 28 (1995) )

5 Comparison of Optical and Electron Microscopes Light Microscope source 1 st condenser TEM SEM or STEM 2 nd condenser Viewing screen Or CCD CA condenser aperture OA objective aperture SA selected area aperture specimen Objective lens Projector lenses Image formed by scanning a small spot Viewing screen Or CCD

6 Inside a Transmission Electron Microscope High tension cable ( kv) Filament condenser aperture Accelerating stack Double condenser lens objective aperture Sample sits here Selected area aperture Viewing chamber

7 An Electron Lens

8 An Electron Lens

9 Geometric Optics A Simple Lens Focusing: angular deflection of ray α distance from optic axis θ x x Object plane front focal plane Lens at z=0 Back focal plane image plane

10 Geometric Optics A Simple Lens Wavefronts in focal plane are the Fourier Transform of the Image/Object θ 1 θ 1 x x Object plane front focal plane Lens at z=0 Back focal plane image plane

11 X-ray and Electron Diffraction from a Silicon Crystal Bragg s Law: n λ = d sinθ 10 kev x-rays 200 kev Electrons λ=1.54 Å λ=0.0251å In Si d 220 = 1.92 Å

12 Electron Velocity and Wavelength De Broglie Wavelength: λ = h p Where h is Planck s constant And p=mv are the momentum, mass and velocity of the electron If an electron is accelerated through a potential ev, it gains kinetic energy mv = ev So the momentum is mv = 2meV Electron wavelength λ = 2 h 1. 23nm = 2meV V (V in Volts) ( relativistically correct form: 2 h c ev (2m c λ ) = ev )

13 Electron Wavelength vs. Accelerating Voltage Relativistic Non-relativistic Accelerating Voltage v/c λ (Ǻ) λ (Angstroms) V 100 V 1 kev 10 kev 100 kev kev 300 kev MeV Electron Kinetic Energy (kev)

14 Resolution Limits Imposed by Spherical Aberration, C s (Or why we can t do subatomic imaging with a 100 kev electron) Lens C s >0 Plane of Least Confusion C s =0 d min Gaussian image plane For C s >0, rays far from the axis are bent too strongly and come to a crossover before the gaussian image plane. For a lens with aperture angle α, the minimum blur is d = min C s α Typical TEM numbers: C s = 1 mm, α=10 mrad d min = 0.5 nm

15 Resolution Limits Imposed by the Diffraction Limit (Less diffraction with a large aperture must be balanced against C s ) Lens α 0 d 0 d 0 Gaussian image plane The image of a point transferred through a lens with a circular aperture of semiangle α 0 is an Airy Disk of diameter 0.61λ = n sinα (for electrons, n~1, and the angles are small) λ α (0.61 for incoherent imaging e.g. ADF-STEM, 1.22 for coherent or phase contrast,. E.g TEM) 0

16 Balancing Spherical Aberration against the Diffraction Limit (Less diffraction with a large aperture must be balanced against C s ) For a rough estimate of the optimum aperture size, convolve blurring terms -If the point spreads were gaussian, we could add in quadrature: d 2 tot d d 2 s 0.61λ = α C α s Probe Size (Angstroms) 10 1 d s d α (mrad) d = Optimal aperture And minimum Spot size 1/ 4 3/ 4 min 0. 66C s λ

17 Balancing Spherical Aberration against the Diffraction Limit (Less diffraction with a large aperture must be balanced against C s ) A more accurate wave-optical treatment, allowing less than λ/4 of phase shift across the lens gives Minimum Spot size: d = 1/ 4 3/ 4 min 0. 43C s λ d = 1/ 4 3/ 4 min 0. 61C s λ (Incoherent image - e.g. STEM) (coherent image - e.g. TEM) Optimal aperture: α opt = 4λ Cs 1/ 4 At 200 kv, λ= Ǻ, d min = 1.53Ǻ and α opt = 10 mrad At 1 kv, λ=0.38 Ǻ, d min = 12 Ǻ and α opt = 20 mrad

18 Electron Diffraction and Imaging a [100] Silicon Crystal Image Diffraction Pattern λ=0.0251å In Si d 220 = 1.92 Å

19 Depth of Field, Depth of Focus D = 0 d tanα 0 For d=3nm, α=10 mrad, D 0 = 300 nm For d=200nm, α=0.1 mrad, D 0 = 2 mm!

20 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.

21 Caustics in a Lens On-axis Tilted

22 Caustics (remove extreme rays and caustics by putting in an aperture) From Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations by J. F. Nye

23 Common Aberrations Astigmatism -x&y focus at different planes -fix by adjusting stigmators Bad Coma -beam is tilted off axis -fix by centering aperture Bad -Δf Δf=0 +Δf Good Good Check lens alignment by going through focus (change lens strength)

24 Lens Alignment Correcting for a gun shift misalignment How do we align one lens, when all lenses are misaligned? Step 1: Strongly excite C1 (small spot size) cross-over moves to lens & optic axis. Use beam shift D2 to bring spot to to axis below C2 Step 2: Weaken C1 (large spot size) cross-over moves away from optic axis Use gun shift D1 to bring spot to to axis below C2. Iterate until spot stops moving

25 Focusing using Fresnel Fringes 2 μm underfocus In focus 2 μm overfocus bright fringe Minimum contrast dark fringe Check lens alignment by going through focus (change lens strength)

26 Correcting Objective Astigmatism using Fresnel Fringes Astigmatic & best focus Stigmated& focused dark fringe bright fringe

27 Materials Microscopy Resources on Campus ( Type Atomic Force Microscopy Applications Topographic Imaging on wafers Accurate height measurements on flat surfaces (~ 0.5 nm vertical) Lateral Resolution 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 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)