Measurement of the energy-spread contribution to information transfer limits in HR-TEM Page: 2 of 3
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ICEM-15, Durban, South Africa (2002).
MEASUREMENT OF THE ENERGY-SPREAD CONTRIBUTION TO
INFORMATION TRANSFER LIMITS IN HR-TEM
Michael A. O'Keefe*, Peter C. Tiemeijer and Maxim V. Sidorov
*National Center for Electron Microscopy, LBNL, Berkeley, CA 94720, USA
FEI Electron Optics, PO Box 80066, 5600 KA Eindhoven, The Netherlands
Advanced Micro Devices, P.O. Box 3453, M/S 32, Sunnyvale CA 94088, USA
Sub-Angstrom TEM of materials at intermediate voltages requires the use of techniques
such as focal-series reconstruction or electron holography (until correction of spherical
aberration becomes routine). Consequently, the information limit of the intermediate-
voltage microscope becomes more significant than its native (Scherzer) resolution. With
a Scherzer resolution of 1.7A, but a sub-Angstrom information limit, the one-Angstrom
microscope (OAM) project at the NCEM is able to generate resolution below 0.8A.2-3
This resolution comes from using the Philips/Brite-Euram computer software by Coene
and Thust4-5 to process experimental focal series of images (containing sub-Angstrom
information) obtained with a modified CM300FEG-UT. The sub-Angstrom resolution
produced by the OAM has been used to image structures containing light atoms 1-3, 6 as
well as ceramics7 and structures within semiconductor devices.8
HRTEM resolution is defined by the first zero in the phase-contrast transfer function
(CTF) at optimum defocus. Microscope information limit d comes from damping of the
CTF by the temporal coherence envelope exp{-%x 22A2u4}, where k is electron wave-
length, Jul is spatial frequency, and A is spread of focus. Information limit d = (7rA/2)
is the inverse of the spatial frequency Jul at which E (u) falls to 1/e2 (fig. 1).
Spread of focus is usually estimated from = CGS{( 2(E)/E2 + 2(V)/V2 + 4 2(1)/12} 1-3 Cc
is the chromatic aberration coefficient and (E)/E, (V)/V, and (I)/I are fractional root-
mean-square (rms) variations in beam energy spread, high voltage, and lens current over
the time of image acquisition. However, E and V terms have contributions that add
linearly as well as quadratically.9 In practice, total beam energy spread (combined E and
V terms) can be measured with a spectrometer such as a Gatan Image Filter (GIF), then
computed by adding rms lens current ripple in quadrature and applying Cc. The problem
is to get the best estimate of the actual energy spread from the GIF measurements. For
the OAM, GIF measurements of the beam-energy spread fall from 0.93eV FWHH at 4kV
extraction voltage to 0.6eV FWHH at zero (fig.2a).
From the GIF, energy spread is EGIF = f{E, + V2 + Gab2 + Gpsf2 + G2} + GIGO + Vr + EB
where E1 is the intrinsic gun spread; V~ is HT noise; Gab, Gpsf, and G~ are GIF aberrations,
point-spread function and noise; GIGO is the contribution from 180Hz stray fields; Vr is
HT ripple and EB is the Boersch contribution. The FEI ZrO2/W Schottk gun at 1800K
has intrinsic energy spread at zero extraction voltage of 0.37eV FWHH. High-tension
(HT) noise contributes 0.leV, as does the HT ripple. The Boersch effect is 0.1eV at 4kV.
GIF aberrations and noise each contribute 0.2eV, and the point-spread function from 2-
pixel broadening is about 0.1eV at 0.05eV/pixel. 180Hz stray fields from the microscope
surroundings typically contribute in the range of 0.01 to 0.05eV.
From these values, EGIF is 0.60 to 0.64eV at zero extraction voltage, and 0.93 to 0.97eV
at 4kV. The lower values agree with measurements from the OAM GIF (fig.2a) allowing
us to estimate the actual beam spread. At 4kV, Ebeam = 'f{E + V2} + Vr + EB = 0.85eV
FWHH. From this value we are able to form the rms energy spread, add it to the lens
current ripple, and compute the OAM spread of focus as 19.6A and the information limit
as 0.78A (fig.2b). This information limit has been confirmed experimentally.2-3
According to the above analysis, the beam energy value to be used in deriving the spread
of focus for the experimental microscope beam can be estimated from the GIF
measurement via Ebeam = f{(EGIF --Giso --Vr-EB) --Gab --Gpsf2 -G2} -+ Vr+ EB.
We emphasize that our values are estimates for the NCEM OAM and depend strongly on
age and condition of the Schottky emitters0, on microscope environment (noise and stray
fields)", and on alignment of the GIF (especially focus and stray field compensation).LBNL - 49677
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O'Keefe, Michael A.; Tiemeijer, Peter C. & Sidorov, Maxim V. Measurement of the energy-spread contribution to information transfer limits in HR-TEM, article, February 18, 2002; California. (https://digital.library.unt.edu/ark:/67531/metadc736388/m1/2/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.