How to optimize your EELS experiments by adjusting the collection angle of your spectrometer ?

 by Alan Maigne, Gatan

I) What is the collection angle?

 

In EELS experiments, it is not possible to collect all the electrons scattered by the sample. Those limitations are mainly due to geometrical factors. As shown on fig.1, there are two important angles to consider if one wants to understand which scattered electrons have been collected in the spectrometer.

Fig.1. Definition of α and β in a (S)TEM. α is called the convergence semi-angle and is determined by the microscope’s settings, especially the condenser lens and aperture. The α angles corresponding to the different configuration of your TEM should be provided by the TEM manufacturer or measured using a known diffraction pattern (cf. Fig.3.) β is called the collection semi-angle and is determined by the objective aperture, the spectrometer entrance aperture, the camera length and the mechanical specification of the instrument. (This article will explain in detail how to measure β for different configurations).

II) How does the collection angle affect my experiments?

Fig.2. Calculation of the fraction of signal collected as a function of the collection angle for 200keV primary electrons. For example, by looking at the high energy Au-M edge (2200eV) with a collection semi-angle of 10mrad, you will collect only 28% of the total available signal, making its detection very difficult, while the same collection angle will achieve 90% collection for the low-energy Si-L₂₃ edge (99eV).

In EELS, the spectrometer measures the number of electrons that have lost a specific amount of energy. The excitation of atoms in the sample will result in characteristic edges in the measured spectrum. The intensity of those edges is directly proportional to the number of atoms present and the scattering cross section of the studied element.  The cross section is a function type of edge and depends strongly on the scattering angle. The fraction of signal collected for a particular transition (edge) varies as shown in Fig.2.

It’s critical to have a collection angle large enough to collect an important fraction of the desired scattered signal. Moreover, because the cross section’s angular dependence varies significantly between elements, β can have a strong influence on the quantification calculation. Digital Micrograph’s quantification function automatically calculates the scattering cross section based on the value of β entered by the operator (we will show later in this article how to save the value of β in DM).

However, it is typically not desirable to collect all of the scattered electrons.  Undesirable signals such as the continuum background for core-loss edges or guided wave modes in low-loss signals² also have a strong angular dependence.  For the case of the continuum background under core-loss edges, the background signal will increase faster than the desired elemental signal the collection angle is increased, resulting in a drop in the signal-to-background ratio as the collection angle is increased. This ratio, also known as the jump ratio, will be highest at small collection angles.  However, the signal-to-noise ratio will be low at small collection angles due to the decrease in the total collection angle.  An optimization can be performed to minimize the uncertainty in the collected signal through Gatan’s EELS Advisor Software (http://www.gatan.com/software/eels_advisor.php)³ but as a general rule of thumb, an appropriate collection angle for your experiment is about three times the characteristic scattering angle for the edge energy under consideration.

TIP 1: An easy way to know how large the collection angle, β , should be for your experiment is to evaluate the characteristic angle for a particular energy-loss event, θ_E=Ee_dge/2E₀,  where E_edge is the transition edge energy and E₀ is the energy of the incident electron beam. With a β ~ 3 θ_E, it’s usually possible to collect about half of the signal, which should be appropriate for most of applications.

III)  Measure of the collection semi-angle β

EELS experiments can be performed either in imaging mode or in diffraction mode (with STEM being equivalent to diffraction mode). Due to the different optics of these two modes, the collection angles are defined by different parameters.

Diffraction (or STEM-EELS) mode

The optical configuration of diffraction or STEM mode is similar to that shown in Fig.1, and the amount of scattered beam collected is limited by the spectrometer entrance aperture,

β=(Radius of the spectrometer aperture) / (Camera length × Geometric factor)

The geometric factor is due to the difference between the position of the microscope film plane and that of the spectrometer aperture and is independent of the microscope’s lens values. Therefore, it is possible to determine the value of β for any camera length or any spectrometer aperture by using this formula. However, some microscopes have poorly defined or calibrated camera lengths (especially in STEM mode), the value of the camera length is usually unknown and β should be directly measured. Even for systems were the value of the camera length shown on the microscope control screen varies a little from the effective value, if very accurate values of β are required, it is better to measure β for every camera length used.

There are two methods to directly measure the collection angle in diffraction mode: the quick method requiring the value of α and the “diffraction pattern” method (available only for GIF).

The “diffraction pattern” method. (only possible with GIFs)

Using the desired camera length (or choosing the “EELS” option of your microscope), observe a diffraction pattern of a known structure on your GIF camera. Looking at the shadow of the entrance aperture, the collection angle, β, can be determined using the known diffraction pattern as a reference to calibrate your image. Even α can be obtained by measuring the size of the diffraction spot as shown on Fig.3.

Fig. 3. Measuring angles with a GIF camera: d is the crystal spacing distance λ is the wavelength of the illumination beam.

λ can  be easily calculated using the restrained relativistic mechanic formula¹.

For example λ(120kV)=3.35.10^-12 m and λ(200kV)=2.51.10^-12 m. 

Common lattice spacings are: Si(111) = 3.135.Å,  Au(002) =0.204 Å

TIP 2: While you are using the diffraction pattern method, it is very easy to also calibrate your CCD camera for reciprocal space (e.g., Diffraction patterns),  To do this, go to Microscope/ Calibrate device from Image and put the red line from the center of the unscattered beam to one of the diffraction spots and follow the instructions. (cf Help file in Digital Micrograph)

 

The quick method

This method can be used with either an ENFINA or a GIF but requires the value of α to be known.

1)  While viewing a 2-d image of the spectrometer CCD (cf screenshot 1), record the ZLP (Zero Loss Peak) with the smallest entrance aperture (1mm for Enfina), without any binning and with a very fast exposure time (0.05s for Enfina).

              

Screenshot 1. Select Show original camera image in the EELS acquire set up option window to have the original two-dimensional CCD image displayed in addition to the spectrum readout during View mode. Note that the image will not be calibrated in spectral units, and also will have hardware binning applied as specified in the Detector Setup group.

Measure L₁ the height of the ZLP of the camera (in pixels) as shown on Fig.4.

 

Fig.4. Image of the ZLP on the detector with the 1mm aperture on the left and the 2mm on the right

 

L₁=2×β(1mm)×K where K is a constant.

 

	2)	Repeat the procedure with the second smallest aperture (2mm). If the beam is still cut by the aperture, L2 = 2 L1.
		-  If L2< 2 L1 , it means the unscattered beam is no longer limited by the entrance aperture but by the convergence angle of the beam. Therefore, the observed beam is the direct image of the unscattered beam and L2 = 2 α K.
		β(1mm)=L1 ⁄L2 ×α
		- If L2 = 2 L1, use a larger aperture (n mm) until the beam is no longer cut by the entrance aperture. Once the aperture is big enough, measure LN
		β(1mm)=L1⁄LN ×α
		The collection angle for an y mm large aperture (y mm) will then just be y. β(1mm) There are two potential problems with this method. L1 = L2 Here the convergence angle is less than the collection angle even at the smallest spectrometer aperture. In this case, try making the measurement with a slightly larger condenser aperture. The beam width LN is determined by the spectrometer aperture even for the largest aperture.  In this case, try making the convergence angle smaller by using a slightly smaller condenser aperture.

EFTEM mode (TEM in image mode)

In image mode, a magnified image of the sample is shown on the screen and the entrance aperture of the spectrometer is conjugate with the sample plane and therefore defines the image area. The angular distribution of electrons entering the spectrometer aperture is independent of the spectrometer entrance aperture size. The angular distribution is limited by the objective aperture of the microscope.  The objective aperture is located in the diffraction plane of the microscope where it limits the angular distribution of the scattered electrons that form the image. Therefore in EFTEM, β is determined by the size of the objective aperture. (cf. Fig.5).

 

Fig.5.Schematic diagram showing how the collection angle in image mode is governed by the objective aperture

If you don’t use an objective aperture, the collection semi-angle is very large (>100 mrads), which means that the scattering cross section becomes independent of β and therefore, it is not necessary to evaluate β. You can set the collection angle to 100mrad in Digital Micrograph.

If you insert an objective aperture and know its diameter (D_obj) and the focal length of the objective lens (f_obj), simple geometrical consideration shows that:

β=D_obj⁄(2.f_obj )

If those values are unknown or if you need an accurate determination of β, it is necessary to measure it.  You can use the following method which is similar to the “diffraction pattern” method explained previously.

Start with the TEM in diffraction mode and record a diffraction pattern of a known material (typically using the GIF, but any recording device will do).  Use any camera length that is convenient; this will not affect the results. This diffraction pattern will be used as a reference to calibrate your imaging device.  Insert the first objective aperture and record a shadow image of the aperture.  Looking at the shadow of the objective aperture, β can be determined using the diffraction pattern of the structure as a reference to calibrate your image as shown on Fig.6.

 

Fig.6. Measuring angles with a GIF camera d is the crystal spacing distance λ is the wavelength of the illumination beam. The calculation of λ is calculated previously in this article.

IV) How to use the value of the collection angle in Digital Micrograph.

As shown previously,  the value of the collection angle varies in function of the TEM mode (EFTEM or DIFF/STEM-EELS), of the objective aperture size for EFTEM and the spectrometer entrance aperture size for DIFF/STEM-EELS. If you are using more than one or two configuration it may be useful to prepare a table as shown on table.1 summarizing the value of the collection angle for different parameters.

TEM Diffraction Mode (200kV)    Entrance aperture (mm)  L(mm)  1  2 3   35 11.0 22.0   33.0  46  8.4 16.7  25.1  68  5.7 11.3  17.0   100  3.8 7.7   11.5  150  2.6 5.1  7.7   200  1.9 3.8   5.8	Table 1. Example of table of collection angle data in different operating modes   TEM Image Mode Objective aperture (mm)  1  2 3  4 Out 4,0 8,0  12,0 24,0 1

For non-AutoFilter systems, to insert the value of the collection angle in Digital Micrograph, you need to click on the EELS Acquisition floating palette set-up button and select Experimental Conditions.(cf screenshot 2 ). The values set in the Experimental Conditions dialog are automatically transferred to all subsequently acquired spectra, making this information available to the analytical routines. For AutoFilter system, select Experimental Conditions in the EELS menu. (cf screenshot 2)

	Screenshot 2. Experimental Conditions windows for AutoFilter (Top) and non AutoFilter (Left) system

If you want to use another value for β, you can either change it in the previous window or change it after the acquisition from the obtained spectrum (or spectrum image) window. To do this, right click the spectrum window and select Image Display/Spectrometer Info and change the value of β, then click on ok. In order to assign, definitively, the new value of β to the file, it is necessary to save the spectrum (or spectrum image) again.

Screenshot 3. How to change the collection angle after acquisition.

As part of spectral analysis, Digital Micrograph will report the value of β used for the calculation in the result window.

 

V) Which collection angle for which experiment?

In EFTEM mode, it is possible to collect EELS data with a large collection angle. However, the spatial resolution can be compromised at lager collection angles by the spherical and chromatic aberration of the image forming lens.  As a general rule, use the same aperture as you would for good HREM imaging.  A smaller aperture will limit the signal collected, while a larger aperture will produce a blurred image.

In STEM-EELS, large aperture will result in high intensity signal but may degrade the energy resolution.  However, as shown in Fig.2., it is critical to have a collection angle higher than the characteristic angle of the observed transition to have a significant SNR. Gatan Enfina and Tridiem systems have aberration correction which allows the preservation of good energy resolution with large entrance apertures. Therefore, using an entrance aperture large enough to satisfy β > 2.θ_E where θ_E=E_edge/2E₀ should be an experiment priority.

Very large collection angles produce an intense signal and are useful for application such as thickness mapping where the entire inelastic signal should be collected.  However, one should not fall into the trap of using too large of a collection angle.  In the case of EFTEM, this will greatly reduce your image resolution and contrast for elemental maps due to TEM lens aberrations.  In spectroscopy, increasing the collection angle will have diminishing returns to the SNR; the signal-to-background ratio falls faster than the gains in shot noise resulting in an overall decrease in the SNR at very large collection angles.

VI) Conclusion

The collection angle plays a key role in EELS experiment for both data analysis and experiment optimization. The collection semi-angle should always greater than 2 or 3 times the characteristic angle of the observed peak. To increase β, it is possible to reduce the camera length and to increase the entrance aperture in Diffraction mode (or STEM). In EFTEM mode without objective aperture, β can be superior to 100mrad allowing you to collect almost any scattered signal. If an objective aperture is used to increase the spatial resolution, β is strongly reduced and using STEM-EELS could be a better solution (but with a much longer acquisition time).

1: R.F. Egerton Electron Energy-Loss Spectroscopy in the Electron Microscope Second Edition Plenum Publishers pp. 437-438

2: N.K. Menon and O.L. Krivanek, "Synthesis of Electron Energy Loss Spectra for the Quantification of Detection Limits," Microscopy and Microanalysis 8 (2002) p. 203

3: R.F. Egerton Electron Energy-Loss Spectroscopy in the Electron Microscope Second Edition Plenum Publishers pp. 194-196.