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Fundamental Theory of Transmission Electronic Microscopy by Yong Ding
The smallest distance between two points that we can resolve by our eyes is about 0.1-0.2 mm, depending on how good our eyes are. This distance is the resolution or resolving power of our eyes. The instrument that can show us pictures revealing detail finer than 0.1 mm could be described as a microscope. The Rayleigh criterion defines the resolution of light microscope as: , where Based on wave-particle duality, we know that electron has some wave-like properties: . If an electron is accelerated by an electrostatic potential drop eU, the electron wavelength can be described as: If we take the potential as 100keV, the wavelength is 0.0037nm. The resolution of electron microscope should be better than that of light microscope.
- Illumination system. It takes the electrons from the gun and transfers them to the specimen giving either a broad beam or a focused beam. In the ray-diagram, the parts above the specimen belong to illumination system.
- The objective lens and stage. This combination is the heart of TEM.
- The TEM imaging system. Physically, it includes the intermediate lens and projector lens.
Because the average distance between two successive incident electrons is around 0.15mm (taking 100keV as the accelerate potential), which is far great than the TEM specimen thickness (~100-500 nm), we can consider the interaction between electrons and specimen as single electron scattering event. From the wave-particle duality point of view, the incident electron can be expressed as a plane wave . Resolving the Schrödinger equation, we can get the departure electron wave function as: Taking Mutt approximation: the amplitude of the scattering beam is the Fourier transform of the specimen's potential. If we considering perfect crystal, its potential can be described as: S The Fourier transform of the potential is: where V g is the structural factor and The diffraction intensity can be calculated as: There are two basic modes of TEM operation, namely the bright-field mode, where the (000) transmitted beam contributes to the image, and the dark-field imaging mode, in which the (000) beam is excluded. The size of the objective aperture in bright-field mode directly determines the information to be emphasized in the final image. When the size is chosen so as to exclude the diffracted beams, one has the configuration normally used for low-resolution defect studies, so-called Diffraction contrast is a dominant mechanism for imaging dislocations and defects in the specimen. However, the resolution of this imaging technique is limited to 1-3 nm. Diffraction contrast mainly reflects the long-range strain field in the specimen and it is unable, however, to provide high-resolution information about the atom distribution in the specimen. The diffraction of electrons is purely a result of the wave property of particles. The The calculation of electron wavelength has been performed in section 1, however, without consideration the perturbation of the crystal potential on the electron kinetic energy. If the electron is traveling in a crystal, which is characterized by an electrostatic potential field V(x,y,z), the equation should be modified as Therefore, the structure perturbed electron wavelength can be obtained. The effective where an approximation of V << U The Therefore, the effect of the potential field is represented by multiplying the wave function by a phase grating function This is known as the |