High-resolution transmission electron microscopy
[1][2] It is a powerful tool to study properties of materials on the atomic scale, such as semiconductors, metals, nanoparticles and sp2-bonded carbon (e.g., graphene, C nanotubes).
While this term is often also used to refer to high resolution scanning transmission electron microscopy, mostly in high angle annular dark field mode, this article describes mainly the imaging of an object by recording the two-dimensional spatial wave amplitude distribution in the image plane, similar to a "classic" light microscope.
One of the difficulties with high resolution transmission electron microscopy is that image formation relies on phase contrast.
The latter can be estimated from the so-called Thon ring pattern appearing in the Fourier transform modulus of an image of a thin amorphous film.
However, a large part of the structure information of the sample is contained in the phase of the electron wave.
The phase change φe(x,u) relative to the incident wave peaks at the location of the atom columns.
If one takes into account only spherical aberration to third order and defocus, χ is rotationally symmetric about the optical axis of the microscope and thus only depends on the modulus u = |u|, given by where Cs is the spherical aberration coefficient, λ is the electron wavelength, and Δf is the defocus.
The aperture function cuts off beams scattered above a certain critical angle (given by the objective pole piece for ex), thus effectively limiting the attainable resolution.
However it is the envelope function E(u) which usually dampens the signal of beams scattered at high angles, and imposes a maximum to the transmitted spatial frequency.
E(u) can be described as a product of single envelopes: due to Specimen drift and vibration can be minimized in a stable environment.
These two envelopes determine the information limit by damping the signal transfer in Fourier space with increasing spatial frequency u where α is the semiangle of the pencil of rays illuminating the sample.
The temporal envelope function can be expressed as Here, δ is the focal spread with the chromatic aberration Cc as the parameter: The terms
The TEAM project at Lawrence Berkeley National Laboratory resulted in the first transmission electron microscope to reach an information limit of <0.5 Å in 2009 [7] by the use of a highly stable mechanical and electrical environment, an ultra-bright, monochromated electron source and double-hexapole aberration correctors.
Thus by choosing the right defocus value Δf one flattens χ(u) and creates a wide band where low spatial frequencies u are transferred into image intensity with a similar phase.
For the CM300 at NCEM, Cs = 0.6mm and an accelerating voltage of 300keV (λ = 1.97 pm) (Wavelength calculation) result in ΔfScherzer = -41.25 nm.
The point resolution of a microscope is defined as the spatial frequency ures where the contrast transfer function crosses the abscissa for the first time.
Contributions with a spatial frequency higher than the point resolution can be filtered out with an appropriate aperture leading to easily interpretable images at the cost of a lot of information lost.
Gabor defocus is used in electron holography where both amplitude and phase of the image wave are recorded.
The Gabor defocus can be expressed as a function of the Scherzer defocus as To exploit all beams transmitted through the microscope up to the information limit, one relies on a complex method called exit wave reconstruction which consists in mathematically reversing the effect of the contrast transfer function to recover the original exit wave φe(x,u).
To maximize the information throughput, Hannes Lichte proposed in 1991 a defocus of a fundamentally different nature than the Scherzer defocus: because the dampening of the envelope function scales with the first derivative of χ(u), Lichte proposed a focus minimizing the modulus of dχ(u)/du[8]
