_____________________________________________________________________________ 6. Transmission Electron Microscopy (TEM) Dr Indranil Bhaumik In a conventional transmission electron microscope, is EM in transmission mode.
Ernst Ruska and Max Knoll built the first electron microscope in 1931 (Nobel Prize to Ruska in 1986) Electron Microscopy (SEM & TEM) bridges the 1 nm – 1 µm gap between x-ray diffraction and optical microscopy Objective lens provides the formation of either image or diffraction pattern of the specimen. The electron intensity distribution behind the specimen is magnified with a three or four stage lens system.
Acceleration voltage determines the velocity, wavelength and hence the resolution of the microscope. TEM with voltage as high as 3 MV is available. Wavelength with relativistic correction:
1
Some real machines
JEM 1.25 MeV
Zeiss HRTEM
2
Components of TEM # Double Condenser Lens system (Magnetic lens) Its function is to control spot size and beam convergence. Consists of two or more lenses and an aperture (both in SEM and TEM).
* 1st lens (C1):Function of C1 (first condenser lens), Create a demagnified image of the gun crossover. Control the minimum spot size obtainable in the rest of the condenser system (important for SEM). * C2 the (weak) second condenser lens controls the intensity of the beam * Even an extra lens (C3 or upper objective lens) can produce parallel beam, if required (for diffraction contrast). The condenser aperture controls the fraction of the beam by reducing the convergence angle. It therefore helps to control the intensity of illumination. 3
# Scanning/tilting alignment The use of two sets of deflection coils enable us to translate (scan) the beam across the specimen without apparently changing the angle of incidence to tilt the beam without changing its position on the specimen. Note: Both X and Y deflections are possible. # Objective lens The objective lens forms an inverted initial image at IMAGE PLANE, which is subsequently magnified. (x 50 typical value) In the ‘back focal plane’ of the objective lens a diffraction pattern is formed. # Objective aperture Function: • Select those electrons which will contribute to the image, and thereby affect the appearance of the image • Improve the contrast of the final image. By inserting the aperture or tilting the beam, different types of images can be
4
formed (bright field/ dark field image). [discussed later] # Intermediate lens The first intermediate lens magnifies the initial image that is formed by the objective lens: The lens can be focused on: • Initial image formed by the objective lens, Image formation • the back focal plane of the objective lens Diffraction pattern formed
Diffraction Mode (similar to XRD)
Image Mode (Analogous to slid projector) 5
# Projector Lens Placed after IL. Used for magnification only! Magnification in the electron microscope can be varied from hundreds to several hundred thousands of times. This is done by varying the strength of the projector and intermediate lenses. Not all lenses will necessarily be used at lower magnifications. Sample Preparation: VERY IMPORTANT and most of the time CUMBERSOME step! Sample thickness as thin as ~0.01µm (100 nm): for the electrons to pass through it and create an image. Cut or ground down to a tiny piece of the specimen Further thinned by an ion milling process or use of a focused ion beam [Focused Ion Beam (FIB) milling]. The mechanical thinning (i.e., the cutting or grinding) is required because high energy ion beams typically remove strips of material with thicknesses in the tens or hundreds of nanometers. Electro-polishing (for metals) A specimen is made the anode in an electrolytic cell. When current is passed, the specimen is dissolved from the anode. Ultra-microtomy (for polymers and biological samples) A firmly mounted specimen is moved past a fixed knife of glass and diamond. Note: Biological samples: made of low electron absorbing elements (e.g., C, N); stained with electron-absorbing heavy metal salts provides contrast reveal details of the cells ultra structure. 6
Image formation mechanism in TEM Interaction of electron beam and a ‘thin’ specimen As the electrons travel through the specimen they are either scattered by a variety of processes or they may remain unaffected. nonuniform distribution of electrons emerges from the exit surface of the specimen they contain all the structural, chemical, and other information about our specimen. exploited in TEM imaging
** the spatial distribution (Fig. A) of scattering can be observed as contrast in images of the specimen, ** the angular distribution of scattering (Fig. B) can be viewed in the form of scattering patterns, usually called diffraction patterns (discussed later). A simple (and fundamental) operational step in the TEM is to use a restricting aperture of a size such that it only selects electrons that have suffered more or less than a certain angular deviation. So you as the operator have the ability to choose which electrons you want to use and thus you control what information will be present in the image.
7
*Elastic scattering (same energy as the primary electron) is usually coherent (in certain phase relation), if the specimen is thin and crystalline (think in terms of waves). * Elastic scattering usually occurs at relatively low angles (1– 100), i.e., it is strongly peaked in the forward direction (waves). *At higher angles (> 100) elastic scattering becomes more incoherent. *Inelastic scattering is almost always incoherent and is very low angle (<10) scattering.
Note: in conventional TEM elastically scattered (and coherent) electrons form the image, the inelastic ones create noise. There are some techniques that exploit the inelastically scattered electrons for complete characterization of the sample as they also contain information (ex: EELS).
8
Contrast and intensity: Contrast (C) quantitatively in terms of the difference in intensity (∆I) between two adjacent areas
In practice your eyes can’t detect intensity changes <5% and even <10% is difficult. So unless the contrast from your specimen exceeds >5–10%you won’t see anything on the screen or on the recorded image. However, if your image is digitally recorded, you can enhance low contrast images electronically to levels at which your eyes can perceive the contrast. You generally get the strongest contrast under illumination conditions that lower the overall intensity (see next page).
There are three ways contrast is formed in TEM 1. Mass-thickness contrast (biology and polymer specimens)
2. Diffraction contrast (major image formation mechanisms in crystalline solid)
3. Phase contrast (high resolution image of crystal lattice) 9
# Mass thickness contrast (by elastic scattering) For elastic scattering angular dependence (crudely): P(θ) ∝ Z2/E2 sin4θ The factors affecting electron scattering (hence contrast): • atomic number (Z) • thickness of specimen • density of specimen • opening of objective aperture (size of aperture) • energy of electrons (E) Intensity of electron beam leaving the lower specimen surface. I = I0 exp(-Sρt) where: I is the transmitted beam intensity; I0 the incident beam intensity; ρt the mass-thickness ρ is the density and t is the thickness of the sample S the effective mass scattering cross-section Note: without aperture all the electron scattered at higher angle (inelastic and/or incoherent) comes to image plane increase the intensity and reduce the contrast 10
An animal cell photographed (a) with and (b) without an objective aperture in position
Example: In front of a flashlight, solid and hallow ball both will cast an identical shadow: a solid black disk. Differentiating between a solid ball (left) and a hollow sphere (right) in a transmission electron microscope. This happens because the electron beam passes through the least amount of matter in the middle of a hollow sphere. The darkness of the image is proportional to the electron absorbency properties of the material used.
11
# Diffraction contrast Diffraction takes place in crystalline materials The constructive interference :
n λ= 2d sin θ When the intensity Ir is removed from the primary beam I0 by the Bragg reflection, the image of the respective sample area appears dark. (contrast created by diffraction)
The grains and precipitate image of Al alloy (a) Titling the specimen changes the contrast of grains (b)
Hence: Major Factors affecting TEM Image Contrast
12
IMAGING modes (in diffraction contrast) Formed by selectively allowing only the transmitted beam (Bright Field Imaging) or one of the diffracted beams (Dark Field Imaging) down to the microscope column by means of an objective aperture.
13
TEM BF and DF images of microcrystalline ZrO2. In the BF image (left), some crystals appear with dark contrast. In addition, thickness contrast occurs: areas close to the edge are thinner and thus appear brighter (lower right side) than those far of the edge (upper left side). In the DF image (right), some of the microcrystals appear with bright contrast, namely such which diffract into the aperture. A transmission electron microscope reveals the multiwall nature of the carbon nanotube. Here we see a 10 nm inner diameter
14
# Phase contrast [High Resolution TEM = HRTEM] Both mass-thickness and diffraction contrast are based on the amplitude contrast mechanisms ONLY because they employ only the amplitudes of the scattered waves (more like shadowgraph). Resolution limited to 1-3 nm. HRTEM: Amplitude + phase full information for reconstruction the sample should be thin enough The basic principle : Consider a very thin slice of crystal that has been tilted so that a low-index direction is exactly perpendicular to the electron beam. All lattice planes about parallel to the electron beam will be close enough to the Bragg position and will diffract the primary beam.
atoms
The diffraction pattern is the Fourier transform of the periodic potential for the electrons in two dimensions. In the objective lens all diffracted beams and the primary beam are brought together again; their interference provides a backtransformation and leads to an enlarged picture of the periodic potential. This picture is magnified at magnifications of typically 106. Resolution of 0.2 nm at 1 MeV with 20 nm thick sample possible!
In practice HRTEM is more difficult then the simple theory
15
Incident parallel electron beam
ψ(r) e- wave
interacts elastically with the potential φ(r) of constituents of the sample while passing through the specimen φ(r)
Modulations in phase and amplitude in the electron wave leaving the specimen.
atoms
Exit plane wave q(r) [EPW] from the object contains the information
q(r):EPW
about the object structure. q(r) now passes through the imaging system of the microscope. HOWEVER lenses are not ideal! spherical /chromatic aberration and defocus distort the EPW, leading to a strong blurring of the images. EPW undergoes further phase change!
q′′(r)
(distortion -artifacts) Reconstruction the REAL phase of the wave function is lost upon imaging, meaning an unwanted information loss.
The recorded image is NOT a direct representation of the samples crystallographic structure. 16
High resolution image contrast depends strongly on defocus, astigmatism, beam tilt, crystal tilt, etc. All of these cause the lattice fringes to become stronger or weaker or move. The relationship between the exit wave and the image wave is a highly nonlinear one and is a function of the aberrations of the microscope. It is described by mathematical function called the contrast transfer
function (CTF). Model CTF, process the final exit wave to reconstruct the original image.
q′′(r)
CTF
φ(r) real image
Twinned BaTiO3
Many ways to find CTF! (beyond scope of the syllabus)
17
Ex: Focal-Series Reconstruction (not in syllabus)
[Zandbergen and Van Dyck, Micro. Res. Tech. 49, (2000) 301.] A series of typically 10-20 high resolution images is recorded from the same object area with different values of the objective lens defocus (with known focus steps). EPW is the generating function behind all images. The images are then transferred to a computer, Use “paraboloid method” to solve phase and get the first estimation of the exit-wave function. (Linear information of an image is within the parabola.) The estimated exit-wave function can be iteratively refined by maximum like-hood fitting. (comparison of experimental images and calculated one from the estimated exit-wave function).
18
HRTEM image of Nb4W13O47 along [001]. The inset shows the structural model Brookhaven National Lab accelerating voltage: 3 MV resolution 0.1nm with 20 nm sample thickness
HRTEM is the ultimate tool in imaging defects. In favorable cases it shows directly a two-dimensional projection of the crystal with defects and all. HRTEM can provide information on the local structure.
Small Angle Grain Boundaries
Gold crystal: Each dot is a gold atom three regions where atoms are arranged differently– these are known as grains Images in this chapter are barrowed from : Transmission Electron Microscopy By David B. Williams and C. Barry Carter (Springer) 2009 ed .
19
