# Collection Angle Considerations

To optimize the collection efficiency and spatial resolution of the EELS signal, it is a prerequisite to understand how electron scattering and collection angles can impact your signal.

## Characteristic scattering angles

The scattering process must conserve both energy and momentum. The momentum change perpendicular to the beam is seen as a change in the angle of the electron. Parallel momentum change does not deflect the electrons. The inelastic scattering distribution will have a Lorentzian distribution with a characteristic angle, $$\Theta _{E}$$, given by the approximate relation for high energy electrons:

$$\Theta _{E}=\frac{E_{edge}}{2E_{0}}$$

where

• $$E_{edge}$$ = Edge energy

• $$E_{0}$$ = Primary beam energy

The EELS signal is highly forward scattered, but for higher energy edges, the distribution can become broad. In addition, the Lorentzian distribution has significant tails, it is recommended that the EELS collection angle be set to 3x $$\Theta_{E}$$ to optimize the ratio of signal to background. Larger angles continue to increase the background contribution but have little effect on the edge signal. Note, this recommendation assumes a mostly parallel incident beam and no strong elastic scattering. Larger angles are often necessary when aligned to a zone axis due to the strong elastic scattering to high angles, and for Cs corrected STEM when the convergence angle is often larger than the recommended 3x $$\Theta_{E}$$ above. However, the below graph is a useful baseline to help optimize the collection angle for your individual sample. $$E_{0} = 200 keV$$

Si L

C K

O K

Cu L

Si K

Au M

Ti K

$$\Delta E (eV)\geq$$

99

284

532

931

1839

2206

4966

$$\Theta E (mrad)$$

0.29

0.83

1.55

2.7

5.3

6.4

14.4

$$2\Theta E (mrad)$$

0.58

1.65

3.0

5.4

10.7

12.8

28

$$3\Theta E (mrad)$$

0.86

2.4

4.6

8.1

16.0

19.2

43

Calculated characteristic scattering angles for several common EELS edges for 200 kV electrons.

## Measure the collection angle

Once you identify the appropriate collection angle, you will need to apply this setting on your electron microscope. Below are graphics that outline how to determine the collection angle based on the technique you select.

### STEM and Diffraction mode For a STEM or diffraction mode TEM experiment, the collection angle is determined by the camera length selected and the physical size of the entrance aperture. The geometric factor accounts for the different between of the screen plane and the entrance aperture plane and is commonly 1.3x. However, on many STEM systems, the camera lengths are descriptive (e.g., HAADF 1) rather than actual values. In this case, each needs to be measured and calibrated.

### EFTEM – Imaging mode When there is an image of the sample on the viewing screen or EELS entrance aperture, the collection angles are defined by the size of the objective aperture. This can be easily calibrated by looking at the shadow if the objective aperture while looking at a diffraction pattern of a known sample.

## References

Egerton, R.F. Electron Energy Loss Spectroscopy in the Electron Microscope. Springer. 3rd ed. New York: 2011.