The Basic of Transmission Electron Microscope. Text book: Transmission electron microscopy by David B Williams & C. Barry Carter.

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1 The Basic of Transmission Electron Microscope Text book: Transmission electron microscopy by David B Williams & C. Barry Carter. 2009, Springer

2 Background survey

$resolution : wavelength : refractive index : semi-angle of the lens sin 1, 0.$

3 Microscopy and the Concept of Resolution Rayleigh criterion for visible light microscopy : point resolution : wavelength : refractive index : semi-angle of the lens sin 1, 0.61 For TEM the approximate: 1.22 /

4 Interaction of Electrons with Matter XEDS EELS DF BF

5 Depth of field: a measure of how much of the object that we are looking at remains in focus at the same time. Depth of focus: the distance over which of the image can move relative to the object and still remains in focus Condenser lens apertures (C2) are inserted to narrow the beam and to increase the depth of field of the specimen and depth of focus of the images. In the TEM, the specimen is usually in focus from the top to the bottom surfaces at the same time, independent of its topography, so long as it s electron transparent. The TEM image is 2D projection of 3D specimen!

6 Why use TEM? Atomic level images; information about specimen s chemistry and crystallography. Limitation: Sampling; interpreting transmission images; electron beam damage and safety; specimen preparation TEM should used together with low magnification OM, SEM and XRD to fully solve a materials problem! Thinner is better! Specimen below 100 nm should be used wherever possible, and in HRTEM or electron spectrometry, specimen thickness less than 50 nm or 10 nm are essential.

7 Some fundamental properties of electrons 1.22 /

8 Scattering and Diffraction

9 Basic TEM operation

10 Different kinds of electron scattering from a thin specimen and a bulk specimen TEM SEM Elastic/inelastic -> energy Coherent/incoherent-> in phase Elastic scattering: coherent at low angles (<10 ); incoherent (>10 ) Inelastic scattering: incoherent (<1 )

Scattering and the cross section of scattering Assumption:

more than once Multiple scattering: scattered > 20 times.

the electron travels through the specimen.

11 Scattering and the cross section of scattering Assumption: Single scattering Plural scattering : electron scattering more than once Multiple scattering: scattered > 20 times. total the number of scattering events per unit distance that the electron travels through the specimen. The mean free path: The average distance that the electron travels between scattering events.

12 Comparison of X-rays diffraction and electron diffraction X-rays are scattered by the electrons in a material through an interaction between the negatively charged electrons and the electronagnetic field of the incoming X-rays. Electrons are scattered by both the electrons and nuclei in a materials; the incoming negatively charged electron interact with the local eelctromagnetic fields of the specimen. The incoming electrons are therefore directly scattered by the specimen; it is not a field-to-field exchanges as occurs for the case of X-rays.

13 Fraunhofer diffraction and Fresnel diffraction Fraunhofer diffraction occurs when a flat wavefront interacts with an object. Since a wave emitted by a point becomes planar at large distaces, this is known as farfield diffraction. (Young s slits) electron diffraction patterns Fresnel diffraction occurs when it s not Fraunhofer. This case is also known as near-field diffraction. - images

14 A word about angles We can control the angle of incidence of electrons on the specimen and we will define the angle of incidence as. In the TEM we use aperture or detector to collect a certain fraction of the scattered electrons and we will define any angle of collection as. We will define all scattering angles controlled by the specimen as. This maybe a specific angle, such as twice the Bragg angle (where = 2 B ) or a general scattering angle. So is the scattering semi-angle for diffraction even though it is 2 B.

15 Elastic Scattering

16 Electron particls have a scattering cross section and differential scttering cross section. Electron particles can be scattered through particular angles. (remember our angles are semiangles). The Electrons interact with the nucleus and the electron cloud throuhg Coulomb forces. We can relate this process to scattering of other particles such as particles, so lots of analysis can carry over from other systems. Particles and Waves Wave are diffracted by atoms or scattering centers How strongly a wave is scattered by an atom is determined by the atomic-scattering amplitude. When we gather atoms together into a solid, the diffraction process gets much more complicated but it is central to TEM. We can relate the process to the diffraction of X-rays, so lots of analysis already exists. When we discuss X-ray and electron spectrometry you ll see that we have to use a particle discription. When we discuss imaging, HRTEM and DPs you ll see that we use a wave description.

17 Electron scattering from single, isolated atoms An isolated atom can scatter a high-energy electron by two mechanism. Coulombic interaction within the electron cloud results in low-angle scattering; coulombic attraction by the nucleus causes higherangle scattering (and perhaps complete backscatter when > 90 ). So Z, V, and all affect image contrast and are the three major reasons why you cannot avoid having to study the physics of electron scattering.

18 Collective scattering from many atoms together within the specimen

19 The Rutherford cross section (V, Z, ) Thinner is better!

20 High-angle Rutherford-scattered electron are incoherent 1. The high-angle, forward scattering can be used to form exceptionally high-resolution images of a crystalline specimen in which the image contrast is due solely to the value of Z (Z-contrast), not the orientation of the specimen (as in the case for low-angle coherent diffraction. 2. Second (but much less important), the high-angle backscattered electrons (BSEs) can be used to form images of the beam-entrance surface of the specimen, in which the contrast is not only due to differences in Z, but also to changes in surface topography of the specimen (such as SEM-BSE). BSE images are rarely used in the TEM because the BSE signal is small.

21 The atomic-scattering factor The scattering-factor approach is complementary to the Rutherford differential cross section analysis, becasue it is most useful for describing the low-angle (i.e., < 3 ) elastic scattering where the Rutherford model is inappropriate. The Structure factor F( )

22 Diffraction equations n = 2d sin B Bragg s Law Laue equations

24 Assignment Reading and summary (in presentation): deadline is Summary should be made as a teaching presentation, so your peer can learn the topic from your presentation (you may use note for description of content in the slides if needed). Evaluation: everyone get two summaries for evaluation, deadline , before lecture. Home work (not this week)

Conventional Transmission Electron Microscopy. Introduction. Text Books. Text Books. EMSE-509 CWRU Frank Ernst

Text Books Conventional Transmission Electron Microscopy EMSE-509 CWRU Frank Ernst D. B. Williams and C. B. Carter: Transmission Electron Microscopy, New York: Plenum Press (1996). L. Reimer: Transmission