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Published: 22 Oct 2019 · Last updated: 22 Oct 2019
Tags: EBSD
Here we define what is meant by the term 'sensitivity' of an EBSD detector. We show how sensitivity is related to the full-system efficiency (the Detective Quantum Efficiency, or DQE
); that the DQE
is very low for conventional detector designs (which use lens-based optics and CCD image sensors); but that the use of fibre-optics (and a large-area CMOS sensor) in Oxford Instruments' Symmetry® EBSD detector allows for very high sensitivity, approaching that of the ideal detector.
Key words: CMOS-EBSD, sensitivity, DQE, electron gain, QE, numerical aperture, fibre optics
We understand that the 'sensitivity' of an EBSD detector directly affects how well the detector performs over a range of diverse applications. However, although the term 'sensitivity' is often used in reference to EBSD detectors, it has not been well defined and thus quantification and comparison between different detector designs is very difficult.
A generalised illustration for detector sensitivity is given in Figure 1. Sensitivity dictates the amount of 'effort' (in EBSD terms, the electron dose
= beam current * exposure time [at a given kV]) needed to achieve the required 'result' (a solved EBSP at the desired angular resolution). Figure 1 expresses the fact that some application results are harder to achieve than others e.g. achieving high angular resolution or analysing 'difficult' samples which produce only low-contrast patterns, both requiring higher doses than do analyses at lower angular resolution or of 'easy' samples producing high-contrast patterns. So, sensitivity can only be discussed in the context of both the electron dose
and the EBSD application
.
The clear benefits of a higher-sensitivity
EBSD detector are the delivery of the same result
with:
Fig. 1 — Schematic illustration of the relationship between electron dose and desired result for high- and low-sensitivity detectors. Lower sensitivity requires more electron dose to get the same result as for higher sensitivity.
The 'result' in an EBSD experiment is directly related to a quantifiable metric – the signal-to-noise ratio (SNR
) in the camera's image of the EBSP. With increasing electron dose, the SNR
increases, and the Kikuchi band contrast inherent to the back-scattered signal become more discernible in the measured EBSP.
Once the electron dose is high enough, a threshold SNR
is reached and the EBSP can be indexed and analysed to a certain angular precision. Thus, we can replace the generalised schematic for sensitivity ('result' vs. dose, Figure 1) with real sensitivity curves – SNR
vs. dose plots for real EBSD cameras. The key characteristics of such curves are illustrated in Figure 2.
A theoretical ideal detector adds no noise to the EBSP signal (so the SNR
is determined solely by the shot noise inherent to the electron signal at any given dose); its SNR
curve is shown in blue and represents the ultimate limit to sensitivity (the SNR
of a real detector must always be lower than that of the ideal at the same dose, for the reasons discussed below.)
The red curve is that modelled for an example real detector (the lens-coupled NordlysMax):
Fig. 2 — The SNR curve for the ideal detector compared to those derived from models of real detectors: red – NordlysMax (1x1 binning); and green – Symmetry.
Conventionally, EBSD cameras have used an Indirect electron Detection (IeD) scheme, with lens-based optics. Here, an intermediary phosphor is used to convert the back-scattered electron energy into a visible pattern of photons on a screen which is then coupled to an image sensor where they are converted back to electrons for detection. IeD with lenses offers considerable practical advantages for manufacturers (compared to Direct electron Detection, DeD, for example) but suffers from one significant technical disadvantage – the efficiency of detection is very low.
Consider the Quantum Efficiencies (QEs
) of the main elements in the detection chain (Figure 3) – we see that the lens is by far the most inefficient part of the system. Although many photons are generated per electron incident on the phosphor (QE
~ 2500 @20keV), and a high proportion of photons incident on the sensor may be detected (QE
~ 70%), lens-coupling throws away >99% of the photon signal generated at the screen. This results from simple geometric considerations – the lens has a limited numerical aperture (NA, or equivalent f/#) so its acceptance cone sees only a very small fraction of all the photons emitted into the 2π sr forward of the screen.
Considering all elements in a detailed analysis, we define the full-system QE
(or electron gain, G
) as:
G
= # electrons detected per sensor
pixel / # electrons incident per screen
pixel
For the best lens-based EBSD detectors we get (@20keV):
NordlysNano ('sensitive' detector; f/0.7 lens): G
= 3.6
NordlysMax ('fast' detector; f/0.95 lens): G
= 1.0
The efficiency of the NordlysNano lens is exceptional (f/0.7); it was achieved only by careful, customised design and it is not practicably possible to exceed this value. f/0.95 is a more typical efficiency even for 'sensitive' lens-based EBSD detectors.
Fig. 3 — Section through a conventional EBSD camera highlighting the main optical elements, with their QEs.
The electron gain, G
, directly affects the form of the SNR
sensitivity curve, Figure 2. It is useful to consider the Detective Quantum Efficiency (DQE
) which is defined as:
DQE
= (SNRo / SNRi)2
where: SNRi
is the signal-to-noise ratio at the input i.e. signal electrons hitting the screen, carrying only shot noise; and SNRo
is the signal-to-noise ratio at the output of the sensor, with added system noise. Note that DQE
is distinct from the QE
discussed above: QE
is simply about transfer of quanta; whereas, DQE
quantifies how much system noise is added relative to the shot noise inherent to the signal and is a true measure of system sensitivity.
The ideal
detector adds no noise, so that DQE
= 1 at all electron doses.
A real
detector does add noise, so that SNRo
< SNRi
and DQE
< 1.
In the low-dose regime, system noise is significant compared to signal shot noise and the deviation from ideal (Figure 2) depends on the ratio of G
to system noise. High G
is clearly beneficial for low-dose sensitivity.
In the high-dose regime (typical of most EBSD experiments), system noise is not significant compared to signal shot noise and it can be shown that G
alone determines the sensitivity:
DQE
= 1 / (1 + 1/G
)
With Symmetry CMOS-EBSD detector, it has now been demonstrated that the low-G
, low-sensitivity characteristic of lens/CCD-based IeDs can be greatly improved, by replacing the lens with fibre optics and the CCD with a large-area CMOS sensor (Figure 5). In contrast to the low-NA of far-field, lens-based imaging, fibre optics couple closely to both the screen and the sensor, greatly increasing the NA. Fibre optics allow the electron gain, G
, of Symmetry to be more than an order of magnitude greater than that of even the best lens-based EBSD camera (as plotted in Figure 4). Again, high G
confers high DQE
and high sensitivity, determining how closely the SNR
curve approaches the ideal at high dose (Figure 2).
Fig. 4 — Fibre optics (left) couple directly to the object and thus have very high NA. By also using a customised, large-area CMOS sensor, G for Symmetry (right) is more than an order of magnitude higher than that of the most sensitive lens-based EBSD camera.
The threshold between the low-dose and the high-dose (photon-limited) regimes depends on G
and system noise: for Symmetry, modelling shows that it is at just a few nAms; for CCD-based cameras, it also depends on the sensor's binning level. Typical materials and EBSD analyses require relatively high electron doses to achieve the desired 'result' (e.g. 1000pps at >3nA, or 3000pps at >10nA), so with Symmetry we are usually operating in the high-dose regime where the DQE
is well described by the curve in Figure 5.
We see that Symmetry (owing to its high electron gain, G
) has exceptional sensitivity, with DQE
> 95% at 20keV compared to only ~51% for NordlysMax. Note also that the QE
of a phosphor screen is proportional to energy, so G
drops in proportion for EBSD analysis at lower keV. NordlysMax sits on a steep part of the DQE
[G] curve so that its sensitivity drops very significantly at lower energies; in contrast, Symmetry lies on a flat part of the curve so that its DQE
is little different at low energy compared to high energy (Figure 5). Note also that increasing the electron gain further (as may be possible by using simple direct electron detection, for example) offers no significant benefit.
The sensitivity of an EBSD detector is directly related to its full-system QE
(or electron gain) and is best quantified using the DQE
. Individual elements of conventional, indirect EBSD camera systems (such as the sensor or the phosphor) may be quoted as having a high QE
to imply high sensitivity. However, the electron gain is actually limited by the lens used to couple the EBSP from the phosphor screen to the CCD or CMOS sensor; thus, these systems suffer from poor DQE
and sensitivity. With Symmetry EBSD detector, the combination of a large-area CMOS sensor and fibre-optic coupling allows for very high electron gain, with DQE
and sensitivity approaching the ideal for most EBSD experiments. The high sensitivity of Symmetry allows for the high speed of its CMOS sensor technology to be fully exploited, at reasonable beam currents and at low keV.
Fig 5 - High-dose DQE: comparing Fibre optic and lens-based EBSD detectors
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