Scanning Transmission Electron Microscopy Facility
Physics of STEM
A. Probe Size
The probe size in a properly aligned STEM (with a field emission source) is limited by spherical aberration
of the final objective lens and by diffraction. These terms are combined wave-optically to give the beam
profile on the specimen. At optimum defocus, this gives a full width at half maximum (intensity),
d = 0.43 Cs1/4 λ3/4 α = 1.4 ( λ/Cs )1/4
where Cs is the spherical aberration constant of the final objective lens, λ is the wavelength of the electron and α
is the aperture size giving that probe size. For STEM1, Cs=0.6mm (0.6x107 Å), λ=0.06 Å at 40 keV, giving d=2.6 Å with
an aperture size α = 14 mRadian. The beam profile is most straightforward to measure using single heavy atoms on a thin
carbon film and the large angle annular detector (see below). Under these circumstances the atom behaves like a point
scatterer, contributing less than 0.2 Å to the observed distribution. The beam profile should be a modified Airy disk,
with 80% of the total intensity in the central peak. The figure above shows a STEM image of a field of single uranium
atoms on a thin carbon substrate. The atoms tend to space themselves 3.5 Å from their nearest neighbor, giving a
convenient internal length reference.
The incident electron beam interacts with atoms in the specimen in a number of ways which can be used to give image information (contrast).
The STEM forms an image sequentially in time by scanning the probe over a selected area of the specimen in a square raster. At each raster
point any number of independent or related measurements can be made, depending on the capabilities of the detector system. The signals we
normally use are scattering of incident electrons from the nucleus (elastic) or electron shells (inelastic) of atoms in the path of the beam.
Many other signals are generated by the scanning probe and could be used for imaging, such as: phase shift of unscattered electrons,
secondary electrons, visible, U.V. or x-ray photons. All but phase contrast give relatively low spatial resolution or poor signal level.
Some of the signals described above can be used to form an image in a conventional transmission electron microscope (TEM), using a series
of electron lenses to make a magnified real image on a fluorescent screen, film plate or parallel readout detector. The most commonly used
are bright field (one minus elastic scattering outside an aperture) and phase contrast. Energy loss electrons can be used if the microscope
has an energy filter, but only a single energy can be in focus at a time. How can we compare these two types of imaging?
The reciprocity principal applies to any image formed using transmitted or elastically scattered electrons where coherent wave optics applies.
It states that any image which can be formed in one instrument can also be formed in the other by interchanging source and detector (see figure below).
The only difference is the efficiency of signal utilization. For example, phase contrast imaging can be done with STEM using a very small detector
acceptance angle (comparable to the illumination convergence angle in the TEM). This has mainly academic interest at present, since most of the
useful signal would be wasted. Similarly, dark field imaging can be performed in the TEM, but utilizing only about 5% of the available signal.
This observation, as well as practical experience, led to the specialization of STEM for dark-field work, where it excels.
The actual dark-field detector geometry is shown in the figure below. The beam incident on the specimen has a convergence angle of
14mRadian. A bright field (BF) detector collects electrons between 0 and 15 mRadian from the axis. Two annular dark field detectors
measure electrons scattered at small angles (SA, 15-40 mRadian) and large angles (LA, 40-200 mRadian). Each of these dark field
detectors collects roughly 40% of the total elastic scattering. The remainder strikes the bright field detector or passes outside
the range of the large angle detector. These detectors are all scintillators coupled by quartz light pipes to photo-multipliers,
giving close to quantum detection efficiency.
The signal on these detectors is calculated wave optically as follows. We start with a plane wave at the back focal plane of the
probe-forming lens. At that plane we introduce phase shifts proportional to α2 and α4, where α is the convergence angle relative
to the specimen. The α2 term represents the defocus of the lens and α4 term describes the spherical aberration of the lens. A
Fourier transform of this distribution gives the amplitude and phase distribution at the specimen plane. (The square of the amplitude
gives the intensity distribution in the probe.) The specimen is approximated as multiple thin slices with the coordinates of all atoms
in a slice projected onto a plane. The real and imaginary parts of the probe wave function at each atom position are multiplied by the
phase shift (due to screened coulomb potential) of that atom. This is propagated to the next plane and repeated. The wave emerging
from the bottom of the specimen is transformed again to give the amplitude distribution at the detector plane. The square of this
amplitude is called a convergent beam electron diffraction (CBED) pattern. In the case of the annular detectors, the CBED pattern
is integrated over the area of each detector to give the final signal. This procedure is commonly used in materials science where
highly ordered structures give non-intuitive images as a function of focus, tilt, etc. The usual method is to postulate a structure
and compare the calculated image with that observed in the microscope under all available conditions. For biological specimens the
image can be approximated by adding up the contributions of each atom in the beam as if there were no neighbors (incoherent approximation).
This is fairly accurate for the large angle annular detector, but becomes less valid as the scattering angle decreases.
This is especially a problem for dark field TEM which uses very small angle scattering and gives a signal with a strong quadratic
component as a function of thickness.
The figure at the right illustrates the effect of coherent scattering in the case of gold islands evaporated on thin carbon.
The image on the left, (A), uses the signal from the large angle detector and gives the impression that the signal is roughly
proportional to the thickness of the island. The right image, (B, recorded simultaneously), uses the small angle signal and
gives very different intensities depending on the orientations of individual grains in the islands.
The effect of coherent scattering can be described in terms of a coherence volume. This is the space surrounding a single atom
where a second atom could be located to give a total signal 1.4 times the sum of the signals from the two atoms scattering
independently. Note that if the two atoms are very close their scattering amplitudes will add and their total intensity will
be twice the sum of the separate intensities. The shape of the coherence volume is an ellipsoid of revolution with its long
axis along the direction of the incident beam. For a thin ring detector located at the inner edge for the small angle detector
(15 mRadian scattering angle), this volume is roughly 1.5 Å diameter and 1000 Å along the beam direction (volume = 1100 Å3).
At the inner edge of the large angle detector (40 mRadian), this volume is roughly 0.5 Å in diameter and 30 Å high (volume = 4Å3).
In most solids the volume per atom is at least 10Å3, so it is unlikely that two atoms would scatter coherently unless the material
were crystalline with the atoms in a column along the beam direction. This is also a worst-case scenario, since most of the
scattering striking the large angle detector is at larger angles. The situation with the small angle detector needs further study.
There is a wealth of information available but its interpretation is not intuitive. The case of dark field in the conventional
microscope is even more severe, due to the small scattering angles employed.
Dark field STEM is especially effective for visualizing heavy atom labels due to its high contrast and lack of phase contrast artifacts.
C. Mass Measurement
The concept of mass measurement in the STEM is based on the incoherent nature of the large angle scattering signal, described above.
The signal we observe is the sum of the scattering from all atoms irradiated by the beam, irrespective of their mutual orientation.
Since the elastic scattering is from the nuclei, we expect a carbon atom to give the same signal regardless of its chemical bonding
state. Also, it happens that the large angle elastic scattering from atoms of different atomic number is very nearly proportional
to their atomic weight. Therefore the signal from the large angle detector is proportional the local mass traversed by the beam.
Mass measurements are very easy to perform with the STEM. One simply draws a circle or rectangle around the object of interest and
integrates the signal minus background within the area marked. For filaments, dividing by the length gives the mass per unit length
(M/L), a parameter very difficult to determine by other techniques. Mass and M/L of single particles and filaments are valuable in
identifying objects, determining uniformity of a preparation, determining the number of subunits in a complex and comparing native
complexes with material assembled in vitro. Mass mapping, radial mass profiles and radial density profiles give additional information
about the internal arrangement of subunits.
High quality mass measurements require:
1) 1-2 μl of solution at a concentration of 1-100 μg/ml containing the intact complex, in relatively pure form,
2) a thin, flat substrate, 3) a means to attach the complex to the substrate and remove the water without destroying the
sample or introducing contaminants and 4) a microscope with adequate probe size, low dose imaging capability and an adequate
recording system. Given an optimum specimen and microscope, the accuracy of mass measurements is determined by the number
of electrons scattered by the specimen and counted by the detectors. Raising the dose to get better mass accuracy causes
more radiation damage, thereby limiting accuracy. Therefore we strive to protect the specimen as much as we can and use
the available information as efficiently as possible. We normally cool the specimen to -160˚C, which reduces the rate of
mass loss by a factor of four compared to room temperature imaging. At that temperature, we find that a dose of 10 el/Å2
causes mass loss of only 2.5% for protein and less than 1% for nucleic acid. For other types of specimen it is necessary
to perform a dose-response study prior to data collection. Under these circumstances the accuracy of mass measurements
is determined mainly by counting statistics. The graph above shows the expected performance for a spherical particle of
density = 1 as a function of mass in kDa. Particles of 100 kDa are expected to give a standard deviation in mass of 5%
and those of 1 MDa, a standard deviation of 1.5%. For any shape of particle, filament or membrane, estimation of mass
accuracy is straightforward.
Requirements on specimen purity are not stringent as long as the particles of interest are recognizable and easily distinguished
from impurities. The optimum concentration is not predictable in advance, so we normally do a dilution series as the first set
of specimens. Freeze drying generally gives the best compromise between structural preservation and straightforward interpretation.
Air drying works in some cases, but usually results in impurities becoming concentrated around the particle of interest, since it
is the last thing to dry. Air-dried biomolecules cannot normally be re-hydrated and regain chemical activity, whereas freeze-drying
(lypholization) is the normal method for long-term storage of enzymes for later use. It is likely that internal folding motifs such
as α-helices and β-sheets (which are stabilized by interaction with water molecules) are disrupted. However the overall topology
of a complex appears to be preserved to a resolution of 20-40 Å. Preservation of morphology is critical for sorting objects in
the image into categories: particles of interest in various views, control TMV particles, defective particles and impurities.
We discourage discarding particles simply because mass values are outliers. We much prefer to sort particles according to
cleanliness of background and quality of fit to a set of models. The efficacy of this sorting depends strongly on the quality
of specimen preservation.
The substrate used for supporting molecules must be thin, flat, strong, low Z and benign to biological molecules.
The best we have found is 20 Å thick carbon evaporated onto single crystal rock salt (NaCl), floated on water and picked
up with a titanium grid coated with holey film. The holey film windows are 4μ diameter, small enough to keep the thin carbon
from tearing but large enough to give an unobstructed view of most complexes. The thin carbon has some hydrophobic character,
causing some sensitive specimens to denature on its surface. Therefore we are always seeking better substrates or film treatments
to temper this tendency.
Last Modified: June 12, 2009
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