Parameters affecting EELS experiments

3.3.2.1 Energy resolution

The overall energy resolution is mainly a function of the type of electron source, filament emission current, the spectrometer resolution, external fields and the energy dispersion

3.3. Parameters affecting chemical microanalysis 47

at the detector [146]. It is conveniently given by the FWHM of the ZLP for a given experiment.

3.3.2.2 Spatial resolution

In STEM mode, the spatial resolution is determined by eq. 3.6. As discussed previously, elastic scattering causes a broadening (b) of a focused electron probe, by an amount that increases with specimen thickness eventually limiting the spatial resolution of EDX. The effective broadening is less for EELS if an angle-limiting aperture (an SAED aperture) is used to eliminate electrons scattered through larger angles (in imaging or STEM mode). In conventional diffraction mode, the area from which the spectrum is taken is limited by the size of the selected area diffraction aperture (SAED). Nonetheless, the precision of the area selected using the SAED aperture is strongly affected by spherical and chromatic aberration of both the TEM objective and projector lenses. At last, in imaging mode, the diameter D of the analysed area is governed by both magnification M and entrance aperture radius R according to D=(2Rh_v)/(Mh_a)where h_v and h_a are respectively the distance from the projector lens to the viewing screen and spectrometer entrance aperture [146].

3.3.2.3 Signal-to-noise ratio (SNR) and Signal-to-background ratio (SBR)

The SNR or fractional noise is determined by the choice of a suitable detector integration time before data read-out. The integration time is chosen according to the number of electrons arriving at the detector. It is determined by the number of electrons falling on the anlaysed area which is related to: the incident beam energy, the brightness of the source, the emission current, the size of the condenser aperture and the collection angle.

The SBR is dependent on the thickness and the collection angle as discussed below and should increase with the accelerating voltage. The SBR is also known as the “jump ratio”

(see Fig. 3.5).

3.3.2.4 Collection angle

The collection angle should be chosen to ensure that the optical dipole selection rule is respected. It is so when collected electrons have transferred minor momentum (¯h.−→q ∼0 where −→q=−→

k₀-−→

k_f) upon collison with specimen outer shell electrons, limiting the observed electronic transitions to those in which the angular momentum quantum number (l) changes by ±1. Typical collection angles of 10 mrads are used in the high loss regime while smaller collection angles (5 mrads<) are used in the low loss region, in particular

3.3. Parameters affecting chemical microanalysis 48

Figure 3.5 Definition of the jump ratio of an ionisation edge. For information, it should be about 5-10 at the carbon K ionisation edge provided the EELS system is aligned correctly [132].

if dielectric data are acquired. These selection rules originate from restrictions imposed on matrix elements of the electric-dipole operator [146].

3.3.2.5 Deconvolution procedures

With increasing sample thickness, there is an increasing probability of multiple inelastic scattering. This constitutes noise and can mask features in the spectrum. It is however possible to remove this multiple inelastic scattering by Fourier transform deconvolution.

Two techniques are routinely employed depending on the energy-loss range [137]:

• Fourier-log method

• Fourier-ratio method

Fourier-log deconvolution is usually applied to low-loss spectra while the Fourier-ratio method is more suitable for high loss spectra [147]. If the specimen thickness is greater than 1 IMFP, the multiple scattering has appreciable intensity and gives rise to a redistri-bution of counts within the spectrum making features like ELNES or EXELFS difficult to observe. This redistribution of counts can be counteracted by deconvolution pro-cedures like the Fourier-Ratio or Fourier-Log routines detailed. In addition, it is also necessary to deconvolute either an experimental spectrum (recommended) or a modeled zero-loss peak (ZLP) to suppress the effects of the ZLP tail on the spectrum. As with all deconvolution procedures, some noise added to the spectra is unavoidable.

3.3.2.6 Relativistic effects

Relativistic effects, also known as retardation effects, are not widely discussed in the literature. Among those are Cerenkov radiation which gives rise to an additional loss

3.3. Parameters affecting chemical microanalysis 49

visible on an VEELS spectrum as a bump, typically arising in the band-gap energy region of common semiconductors (2 - 3 eV). This occurs as soon as the speed of the probing electron exceeds the speed of light inside the probed medium [148] ( i.e. v>c₀/n, n being the refractive index). Consequently, the VEELS spectrum is spoiled by effects which do not purely stem from the interaction beam/specimen impacting negatively on the accuracy at which band-gap measurements can be performed affecting eventually Kramers-Kronig analysis results. A few possibilities exist to circumvent such losses:

• decrease the accelerating voltage

• record VEELS spectra with a non-zero momentum transfer (−→q 6=0)

• use the difference method described in [149]

The first method is the easiest but is not always experimentally possible (the EELS spectrometer may need some realignment at lower accelerating voltage). The second one is also experimentally difficult but for another reason: the intensity is very weak making the acquisition time much longer. More importantly, optical data from such spectra acquired under those conditions cannot be compared with the standard optical method where −→q ∼0. The third method is the most versatile. The user can still derive optical data from EELS measurements even if decreasing the accelerating voltage is impossible.