General operation and modes of TEM
Purpose of the practicum: acquiring a hands-on experience in TEM operation, understanding
construction of the microscope, alignment procedures, operation in diffraction and imaging modes,
acquisition and basic evaluation of the data.
Results to be achieved: setup for the proper imaging conditions (alignment); experimental recording
of TEM images and diffractions.
Requested theoretical background
Due to the limited operation time at the microscope, participants are advised to be familiar with the
following concepts:
1. Main components and construction of TEM
a. Column and functional components (gun, condenser, objective, projector, apertures,
detector, sample holder, vacuum system)
http://www.microscopy.ethz.ch/TEM-structure.htm
b. Ray paths for different imaging modes
2. Imaging modes
a. Electron beam interaction with the sample, exit wave
b. Thinking in real and reciprocal space
c. Lens as Fourier transformer
d. Diffraction mode
http://www.matter.org.uk/diffraction/
i. Information contained in diffraction pattern
ii. Concept of crystallographic zone axis
e. Imaging mode
http://www.nanoscience.gatech.edu/zlwang/research/tem.html
i. One beam imaging; bright field (BF) and dark field (DF)
ii. Multibeam imaging, lattice images
iii. Lens aberrations
Content of the practicum and consequent report
All the steps of practical operation of the instrument will be explained and shown by demonstrator at
place. Participants will follow up instructions and obtain their own data for further evaluation. It is
advised to have a memory stick for data pick-up.
1. Column alignment
http://www.rodenburg.org/RODENBURG.pdf
a. Gun
b. Condenser
c. Stigmation
d. Optimum defocus
http://www.umsl.edu/~fraundorfp/epc/
Report should contain detailed description of alignment procedure with definition of necessity and
meaning of each step.
2. Diffraction
a. Orientation of Si sample into [110] zone
b. Setup and recording of Selected Area Electron Diffraction (SAED)
Report should contain a description of how to obtain SAED, identification and proof of correct
orientation, identification and measurement of different reflections, estimation of the precision of
measurements.
3. Imaging
a. Setup and recording of BF images at different crystal tilts
b. Setup and recording of DF images at different diffraction conditions
Report should contain a description of setups for BF and DF modes, explanation of crucial
prerequisites for obtaining right images. Origin of the contrast on the recorded images should be
evaluated and explained.
Sources of general information:
http://www.rodenburg.org/guide/index.html
http://www.matter.org.uk/tem/
http://www.unl.edu/CMRAcfem/temoptic.htm
http://www.unl.edu/CMRAcfem/glossary.htm
http://em-outreach.ucsd.edu/web-course/toc.html
http://www.nanoscience.gatech.edu/zlwang/research/tem.html
High Resolution TEM
Purpose of the practicum: acquiring a hands-on experience in TEM operation, understanding of
crucial optical and experimental parameters for imaging, understanding the relation of experiment and
calculation in HRTEM.
Results to be achieved: experimental estimation of instrument parameters (magnification, spherical
aberration and defocus); experimental recording of HR images, estimation of parameters and
theoretical calculation of the images for these parameters.
Description of experiment:
• sample – Si [110] with flat amorphous areas;
• basic alignment of TEM and sample – height, orientation, rotation center, defocus,
astigmatism;
• acquisition of lattice images from a thin crystalline region at ~x300K;
• acquisition of the image time series of amorphous at ~x300K magnification and underfocus ~500nm for Cs-Df-astigmatism determination.
Description of calculations:
• calibration of magnification using images of crystalline areas (DM);
• determination of optical parameters of the microscope using diffractograms of amorphous
areas (DM, Polar transformation script, Gauss filter script, Excel or Origin);
• determination of defocus values of defocus series and calculation of images for estimated
microscope parameters (Df, Cs) and different thicknesses; estimation of the thickness (DM,
EMS).
Theoretical background
Under ideal imaging and sample conditions a HRTEM image is an interference pattern of unscattered
electrons and those scattered by the sample. The interference pattern is affected by phase modulation
introduced by the aberration of the objective lens, i.e. the image is a convolution of the point transfer
function of the objective lens T (r ) with the object exit wave function ψ o (r ) [1, 2, 3, 4 ].
ψ (r ) = ψ o (r ) ⊗ T (r )
(1)
The phase modulation by the objective lens is better understood in the Fourier space at the back focal
plane of the objective lens (Fourier space) where the Fourier transform of the image intensity is given
by
(2)
ψ (q) = ψ o (q)T (q )
With ψ (q ) and T (q) being the Fourier transforms of the object-exit wave function ψ o (r ) and
T (r ) respectively, q is the spatial frequency, and the phase contrast transfer function T (q ) is defined
as
(3)
T (q) = A(q ) Sinχ (q )
where A(q) is an aperture function and χ (q ) is a phase modulation function due to lens aberrations.
Considering only defocus and Spherical aberration, χ (q ) then takes the form:
χ (q) = 0.5πλ3C s q 4 + λπεq 2
(4)
where λ is the wavelength of the electrons, ε is the defocus, C s is the spherical aberration constant.
If we assume the aperture function A(q ) to be = 1, then the function χ (q ) describes the phase
modulation of the exit wave function as it propagates through the imaging system. χ (q) can be
evaluated by analysis of the Fourier power spectrum of high resolution images. Power spectrum of the
image is expressed as
P(q) = ψ (q)
2
(5)
Combining equations (2), (3), (5) we get
2
P(q ) = ψ o A sin 2 χ (q )
(6)
For an amorphous specimen the probability of scattering can be assumed to be constant for all spatial
frequencies therefore the intensity of the power spectrum is defined mostly by the contrast transfer
function
P(q ) ~ sin 2 χ (q )
sin χ takes particular values -1, 0 and +1, when the following condition is met
χ (q) = 0.5πλ3C s q 4 + πελq 2 = n
(8)
π
(9)
2
Thus a power spectrum (radial distribution of intensity of FFT pattern of the image) of the amorphous
specimen, which is proportional to sin 2 χ , will contain minima corresponding to zeros of sin χ and
maxima corresponding to ±1. Each maximum in power spectrum may be associated with odd and
minima with even integer n.
Rearranging and dividing equation (7) by π q 2 gives the linear relationship
n
C s λ3 q 2 + 2λε = 2
q
(10)
If the image is taken at strong under focus conditions ( ε << 0 ) the integer n takes only negative
values and thus Cs and ε can be unambiguously determined as a slope and intersect of linear
n
regression in q2 <-> 2 coordinates.
q
Content of the practicum and consequent report: determination of spherical aberration
coefficient Cs and defocus value
Calculations will be conducted on Digital Micrograph, demo version of the program will be provided
for installation on personal computers.
Experimental part
Alignment of the column.
Acquisition of Si[110] images for magnification calibration. Calibration should be performed at
exactly the same imaging conditions as series acquisition afterwards: the same current of objective
lens and the same magnification ~x300K. Precise calibration of magnification is essential for this task
as far as eq.(10) is written in the units of spatial frequencies, i.e. the scale of q should be known and
the accuracy of default camera calibration is not enough.
Acquisition of the images of amorphous region. Due to the moderate dynamical range of CCD camera
of the microscope the transfer of high spatial frequencies is suppressed by noise. In order to enhance
oscillations of transfer function for high q (get more data points for better linear fit) it is advised to
acquire multiple images at the same place and imaging conditions and average them afterwards. This
will increase signal-to-noise ratio significantly. Images should be acquired at significant underfocus
(~x3 Scherzer focus) in order to produce reasonable number of experimental points (minima and
maxima of the radial intensity distribution).
Report should contain detailed description of experiment with explanation of the meaning of
performed operations.
Calculation part
Calibration of magnification.
•
Start Digital micrograph.
•
•
Under the menu File/Open open the image showing the HRTEM image of Si[110].
To calibrate the image go to Microscope/Calibrate image from diffractogram.
•
Calibrate your image by following the instructions given by the Digital Micrograph software.
•
Use the known values for Si reflections in the [110] orientation (d111=0.314 nm, d200=0.272 nm) to
•
calibrate your image and remember to divide the value by two if you select a pair of reflections.
After calibration of the image note down calibration value of the image in pixel in nm by right
clicking on the image image display/calibration.
•
Close the image.
Estimation of Cs and defocus.
•
Open the experimental amorphous image stack
•
Open the following Digital Micrograph scripts:
•
-
Polar projection.s
Stack align by correlation to average to accuracy and sum.s
-
Gaussian high-low pass filter.s
-
Hanning window.s
Choose Rectangular ROI tool from a toolbox and select ROI dragging the mouse over the stack
image with Alt pressed. Then run “Stack align by correlation to average to accuracy and sum.s”
script (Ctrl+Enter) and wait until you get a drift corrected average image of amorphous region
with reduced noise, this can take some minutes.
•
Select 1Kx1K ROI and copy it to separate window (Ctrl+C, Ctrl+Alt+V). Run “Hanning
Window.s” script and apply 25% hanning in order to hide drift artifacts at the edges. Perform
background subtraction by running Gaussian high-low pass filter.s with parameter equal to -100.
•
Calibrate the image by entering the values you noted from the calibration part of the exercise
(right click, image display/calibration)
•
Calculate the FFT of this image.
20 nm
Hanned and calibrated amorphous image
•
Diffractogram of amorphous image
Calculate power spectrum (diffractogram) by changing the FFT image from complex to real
(Edit/Change data type/real/modulus). Perform background subtraction by running Gaussian
•
high-low pass filter.s with parameter equal to -100.
Open the script “Polar projection.s” and run it on the diffractogram, you should get a projection of
the modumus of CTF function.
Example of polar projection of diffractogram.
Intensity profile of radial distribution.
•
Calculate an intensity profile and integrate to obtain the maxima and minima values for the
•
contrast transfer function CTF.
Correctly assign the n values to each extremum, the wrong assignment will lead to non-linear plot.
•
Draw a plot (in Excel or Origin) in accordance to eq.(10) and determine the values of defocus and
Cs assuming a wavelength for 200kV electrons 0.0025 nm. Optionally estimate the value of
astigmatism.
Report should contain step by step description of calculations illustrated by figures and resultion df
and Cs values.
Relevant references:
[1] O.L. Krivanek, Optik 45 (1976) 97.
[2] W.M.J. Coene and T.J.J. Denteneer, Ultramicroscopy 38 (1991) 225.
[3] P.Buseck, J.Cowley, L.Eyring, High Resolution Electron Microscopy and Associated Techniques,
pp. 546-548
[4] L.J.Allen, W.McBride, N.L. O’ Leary, M.P Oxley, Ultramicroscopy 100 (1991) 91
[5] M.Kuzuya, M. Hibino, J.Electron Microsc. 30,2, (1981) 114-220
[6] K. Wong, E.Kirkland, P. Xu, R. Loane, J.Silcox, Ultramicroscopy 40 (1992) 139-150
Convergent Beam Electron Diffraction
Purpose of the practicum: acquiring a hands-on experience in experimental acquisition of different
CBED patterns (CBED, LACBED, MB-CBED), usage of CBED for orientation of a crystal in a
particular crystal zone, understanding of Kikuchi and HOLZ lines, introduction to an information
content of CBED pattern.
Results to be achieved: setup for the proper conditions for acquisition of CBED pattern in different
modes, getting familiar with reciprocal space and crystal orientation, experimental recording of
TEM images and diffractions.
Requested theoretical background
Basic concepts:
Reciprocal space and reciprocal lattice of a crystal; Laue zones.
Braggs law and a formalism of Evald sphere.
Electron diffraction with parallel illumination.
Kinematical theory of convergent beam electron diffraction.
Higher Order Laue Zone lines and Kikuchi lines.
Schematics for obtaining CBED, LACBED and MB-CBED patterns.
Content of the practicum and consequent report
All the steps of practical operation of the instrument will be explained and shown by demonstrator at
place. Participants will follow up instructions and obtain their own data for further evaluation. It is
advised to have a memory stick for data pick-up.
Si sample oriented roughly in [110] zone will be used.
1. Column alignment
http://www.rodenburg.org/RODENBURG.pdf
a. Gun
b. Condenser
c. Stigmation
2. CBED
Orientation of Si sample exactly into [110] zone using Kikuchi pattern, acquisition of zero
order CBED disks at different thicknesses.
Report should contain a practical consideration of how to obtain a CBED pattern.
3. LACBED
a. Retuning of TEM in nanoprobe mode. Obtaining and recording of LACBED patterns.
b. Orientation of the sample in [230] zone using LACBED pattern and Winkiku
program. Obtaining of LACBED and CBED patterns in [230] zone.
Report should contain explanation of differences of operation in TEM and nanoprobe modes. Why
the last is necessary to obtain LACBED? Description of the procedure for obtaining LACBED.
Explanation of the differences in CBED and LACBED patterns of the same zone.
4. MB-CBED
a. Orientation of the crystal in [110] zone.
b. Setup of experimental conditions and recording of MB-CBED patterns.
Report should contain a description of setup MB-CBED method. How do different parameters
(image height, magnification, convergence angle) influence the pattern obtained?
CBED pattern of Si [110]
LACBED pattern of Si [230]
MB-CBED of Si [110]
Reference literature (provided as pdfs on the web site):
Convergent-Beam Electron Diffraction.pdf
Large Angle Convergent Beam Electron Diffraction.pdf
Simultaneous Observation of Bright- and Dark-Field Large-Angle Convergent-Beam
Electron Diffraction Patterns.pdf
Simultaneous Observation of Zone-Axis Pattern and +-G Dark-Field Pattern in ConvergentBeam Electron Diffraction.pdf
Assessment of the TEM/CBED procedure for strain determination in <130> zone axis.pdf
Three-Dimensional Strain-Field Information in Convergent-Beam Electron Diffraction
Patterns.pdf
Energy Dispersive X-ray spectroscopy
Purpose of the practicum: acquiring hands-on experience in EDX spectroscopy, understanding of the
principles of qualitative EDS analysis, evaluation of EDS data.
Results to be achieved: setup the proper TEM condition for getting EDS spectra, evaluation of
structure and composition of complex semiconductor device.
Background
General
http://www.microscopyanalysis.com/download/449/XRayMicroanalysisTutorial_MAJuly06.pdf
High energy electron interaction with the matter and origin of characteristic X-rays.
http://www.microscopy.ethz.ch/xray_spectrum.htm
http://seallabs.com/hiwedx.htm
http://microanalyst.mikroanalytik.de/info1.phtml
http://microanalyst.mikroanalytik.de/info2.phtml
Working principles and construction of EDX detector.
http://microanalyst.mikroanalytik.de/info3.phtml
http://www.x-raymicroanalysis.com/pages/tutorial1/system1.htm
http://www.x-raymicroanalysis.com/pages/tutorial1/system2.htm
http://www.x-raymicroanalysis.com/pages/tutorial1/system3.htm
Content of the practicum and consequent report
All the steps of practical operation of the instrument will be explained and shown by
demonstrator at place. Participants will follow up instructions and obtain their own data for further
evaluation. It is advised to have a memory stick for data pick-up.
The students will be provided with a cross sectional sample of a complex electronic device
(transistor). The task for the practicum will be to describe the structure of the device and to unravel a
chemical composition of its components.
Report will include TEM images, EDS spectra and a written evaluation of the findings.
Content of the experiment is as follows:
1. Column alignment
http://www.rodenburg.org/RODENBURG.pdf
2. Sample orientation and optimization of conditions for imaging and spectra acquisition.
3. Acquisition of the images and identification of principal components of the device.
4. Acquisition of local EDX spectra from different parts of the sample.
5. Qualitative evaluation of images and spectra using TEM and EDX software.
Dislocation Analysis by means of the Weak-Beam Dark-Field
(WBDF) Method
1. Introduction and Motivation:
When analysing dislocations in a crystal, it can be most important to determine the type of
each dislocation visible in a TEM image. For this purpose it is necessary to determine the
Burgers vector of a dislocation in order to decide if the dislocation is a pure screw, pure edge
or a mixed dislocation. The imaging of dislocations in a TEM is predicated on the diffraction
contrast by exploiting the DF method under special conditions. By using the WBDF method it
is possible to image the dislocation lines and to determine the Burgers vector. In the following
the WBDF technique is described.
2. Basics of the WBDF Method:
In a WBDF image dislocations can be visualized as sharp bright lines, whereas the perfect
parts of the specimen are not visible and appear dark. Thereto the sample and the incident
beam must satisfy specific tilt conditions. The general exposure technique is shown in figure
1.
Objective
Aperture
Figure 1: Path of rays in the TEM for the WBDF method using an edge dislocation as an example. For the
defect-free area the incident beam is far away from the exact Bragg condition (large excitation error). In the
area near the dislocation core (black mark in the specimen) the Bragg condition is exactly satisfied. This is
caused by the bending of the hkl plane near the dislocation core. In the WBDF image the dislocation line
appears as a bright line to dark background.
In principle, the WBDF technique is an on-axis dark field imaging method by using a
diffracted beam with large excitation error for the defect-free sample area. Thus, the defectfree sample area appears dark because of the weak diffraction intensity. However, close to the
dislocation core the hkl plane is bended back into the Bragg condition, which gives rise to a
bright intensity peak (the dislocation line). The main challenge is to adjust the tilt conditions
in the way that the excitation error of the g reflection used is close to zero only near the
dislocation core where the bending of the hkl plane is most prominent. Then a very sharp
dislocation line near the dislocation core becomes visible in the WBDF image.
Three conditions have to be satisfied to get a high quality WBDF image with well
detectable dislocation lines:
-
Beam tilt to on-axis DF and selection of a Bragg spot by using objective aperture
Right adjustment of the excitation error
Two beam conditions to get high contrast
3. Obtaining appropriate Tilt Conditions
In the following description we refer to a [110] AlN cross-section sample, whereas the
principle procedure is the same for other materials. The AlN was grown in the hexagonal
phase (2H AlN, wurtzite structure) on a sapphire (Al2O3) substrate. We want to use the 0002
reflection for the WBDF image.
1st step: Tilt the sample into an appropriate zone axis, in this case [110], as it is shown in
figure 2.
0002
Figure 2: Calculated spot pattern of 2H AlN from the [110] zone axis. The Kikuchi lines are also shown.
2nd step: The next step is to get rid of almost all other reflections with the exception of the
transmitted beam and in this case the 0002 reflection. This means we want to approach the
two beam condition. For this purpose tilt the sample that way, that only that line of reflections
is visible, which contains the 0002 reflection. The tilting condition is shown in Figure 3.
3rd step: Tilting to the so-called 3g condition. Normally the 3g condition is used to get high
quality WBDF images. 3g condition means, that the g reflection you want to use for your
WBDF image (in this case 0002) is in the optical axis, whereas the Bragg condition for the 3g
refection (in this case 0006) is exactly satisfied. Then we get a relatively large excitation error
for the g reflection. This condition is shown in figure 4. To reach this condition we have to
proceed after step 2. First tilt the sample again, however in the opposite direction so that the g
reflection satisfies the Bragg condition exactly. This means, that the g-Kikuchi line intersects
the g-reflection exactly and the –g-Kikuchi line passes the zero spot. Then tilt the incident
beam that way, that the g refection appears in the optical axis. The 3g condition as it is drawn
in Figure 4 is then satisfied. Now the 3g-Kikuchi line intersects the 3g refection exactly and
the -3g-Kikuchi line passes the zero spot.
0002
Line of visible spots
Intersection line of the Ewald sphere with the ZOLZ
Figure 3: Tilt condition after sample tilt out of the zone axis to approach the two beam condition.
4th step: Select the g reflection with the objective aperture and put the image on the screen.
4. Dislocation Analysis and g*b Criterion
As mentioned above, a dislocation bends
v the lattice planes near the dislocation core. This can
be described by av displacement field R . The displacement field generates an additional phase
v
shift ~ exp(2πigR ) of the Bragg diffracted beam, which leads to a diffraction contrast in the
v
v
image. As a rough rule of thumb the displacement vector R is parallel to the Burgers vector b .
Figure 4: 3g condition for the WBDF image. The g refection is in the optical axis with a large excitation error.
You can see this relation qualitatively for the pure edge dislocation in figure 1. In this
illustration
the main part of the displacement near the dislocation core points in the direction
v
vv
v v
v v
of b . The phase shift exp(2 πigR ) only comes into effect if g ⋅ R ≠ 0 . This means, if g ⋅ b = 0
v v
=> g ⋅ R = 0 and the dislocation line is not visible, then the displacement field is parallel to
v v
the exploited hkl plane and does not change the phase. This relation is called g ⋅ b criterion. If
v v
g ⋅ b = 0 , the dislocation line is not visible, otherwise the dislocation is visible in the WBDF
image. This enables the Burgers vector determination and identification of the dislocation
type by taking WBDF images of the same sample area by exploiting different g reflections.
5. Example: WBDF analysis of wurtzite 2H AlN grown on c-plane Sapphire
a) Crystal structure and growth:
AlN can be grown in the hexagonal wurtzite structure on c-plane Sapphire. This structure
3
can be described by means of two hcp lattices, shifted along the c direction by c , as it is
8
shown in figure 5. The a-parameter of bulk AlN is 3.112Å, the c-parameter is 4.982Å.
Figure 5: Hexagonal wurtzite structure of 2H AlN (α-phase)
Figure 6 shows the growth conditions of 2H AlN on c-plane sapphire from the [001]
direction. The inner cell (a=2.747Å) of Al2O3 determines the AlN growth. This gives rise
to a large lattice mismatch of -11.7%, and the AlN receives compressive stress at the
AlN/Al2O3 interface. A strain energy in the AlN lattice is reduced by the formation of
strain induced misfit dislocations, which are normally partial dislocations. These misfit
dislocations can interact with each other, which leads to the formation of threading
dislocations (TDs). The growth of the TDs along the epitaxial growth direction of the
material is not strain induced but growth induced. Thus it is still a big challenge to grow
AlN directly on sapphire.
b) Burgers vector determination in 2H group III-nitrides and g*b criterion
Depending on the crystal structure and therewith depending on the basal plane, only
specific Burgers vectors are possible. The construction of the possible Burgers vectors
results from the displacement of the basal plane along the Burgers vector namely that way,
that we still obtain a valid stacking order after the displacement. Figure 7 shows the
possible Burgers vectors in 2H group III-nitrides and their notation.
BurgersVectors
AB,AC,BC
Notation
Dislocation type
1/3[2-1-10]
DE
[0001]
AB+DE
1/3[2-1-13]
AF
AE
FE
1/3[1-100]
1/6[2-203]
1/2[0001]
perfect dislocation,
a-type
perfect dislocation,
c-type
perfect dislocation,
(a+c)-type
Shockley partial
Frank partial
Frank partial
Figure 8 shows the diffraction patterns from the AlN/Al2O3 interface of the AlN [110] and
the AlN [120] zone axis. The charts below show g*b values for the applicable g
reflections. Referring to the AlN [120] zone axis pattern, only c- and (a+c)-type
dislocations will be visible when using the 0002 reflection. When using the 2-1-10
refection only a- and (a+c)-type dislocations will be observable in the WBDF image. By
imaging the same sample area exploiting two different refections for the WBDF image,
e.g. 0002 and 2-1-10, the Burgers vectors can be determined by means of the exclusion
principle.
Figure 6: Unit cells of AlN and Al2O3 shown in the epitaxial growth direction of [0001]
c) Experimental WBDF Images and Dislocation Analysis
Figure 8: Spot patterns from the AlN/Al2O3 interface of the AlN [110] and AlN [120] zone axis. The
g*b values for the applicable g reflections are also shown.