1084 Dai Tang et al.
Figure 2. Measured beam current and stage current (electron beam incident on Fe matrix), at 10 and 20kV accelerating voltages, and different spot sizes, for a tungsten filament instrument (labeled “ASPEX”) and a Schottky field-emission instrument (XL30).
inclusions. The noise-to-signal ratio (N/S) in the BSE image is inversely proportional to the square root of the total number of BSE detected (n):
N S = ffiffiffinp
n = 1 n=CηIbτ; pn : ffiffiffi (1)
The backscattered signal detected from a given beam location is given by:
(2)
where C is a constant (determined by the size, position and gain of the BSE detector); η the BSE yield; Ib the beam cur- rent; and τ the dwell time per pixel. The beam current (Ib) was measured with a Faraday cup
and the stage current (Is) was measured with the beam incident on polished steel. Measured beam and stage currents are presented in Figure 2, showing the effect of spot size and accelerating voltage for the tungsten filament ASPEX instrument and the Schottky field-emission instru- ment XL30. (“Spot size” is a relative term used by the parti- cular instrument supplier; for the ASPEX instrument spot size is given as a percentage, and for the XL30 instrument as a numerical value from 2 to 7.) The general trends are that the beamcurrent is larger for larger spot sizes, and also depends on accelerating voltage. For the tungsten filament ASPEX, the beam current at 10kV (for the generally used 40% spot size) is ~30% of the beam current at 20kV (and the same spot size). For the field emission XL30, the difference is smaller: the beam current at 10kV (spot size 5; typically used in automated inclusion microanalyses) is ~60% of the beam current at 20kV (spot size 5). The smaller beam current at 10kV would require a
longer pixel dwell time to achieve the same noise-to-signal ratio as at 20 kV. The effect of pixel dwell time on the noise- to-signal ratio was measured as the standard deviation of BSE line scans on steel, setting the same brightness and
Figure 3. Effect of pixel dwell time on the backscattered electron (BSE) image noise-to-signal ratios for imaging at 10 and 20kV for (a) ASPEX instrument (spot size 40%) and (b) XL30 instrument (spot size 5); the effect of accelerating voltage is to change the beam current and BSE detector gain, as shown by normalizing the noise-to-signal ratio with respect to these two factors [(c) and (d); beam current Ib and relative detector gain G are listed in Table 1].
contrast levels. BSE contrast was set using Fe and Al as standards, adjusting the brightness difference (on the dimen- sionless 0–255 brightness scale reported by the instruments) to 100. Measured values (Figs. 3a and 3b) show that the noise- to-signal ratio is approximately proportional to the reciprocal of the square root of pixel dwell time, as expected. For mea- surements on the XL30 (INCA) instrument, extrapolation of the measured values to large dwell times—zero values of 1/τ0.5—indicate non-zero noise-to-signal ratios; this residual noisewas likely caused by some roughness on the surface of the steel sample used for these measurements. For a given pixel dwell time, noise-to-signal ratios were
larger at 10kV than at 20 kV, reflecting the lower beam current at 10 kV, and also the effect of the accelerating voltage on the BSE detector gain. For the solid-state BSE detectors used, the detector gain (G) is approximately proportional to the energy of BSE: that is, the detector gain is expected to be twice as large for imaging at 20kV than at 10 kV, at the same beam current (Goldstein et al., 2003). The beam current Ib (for one spot size as example) and relative BSE detector gain G (20kV relative to 10kV) are listed in Table 1. For monitoring possible changes in instrument condition, it was convenient to measure the stage current with the beam incident perpendicularly on polished steel; the measured stage current was converted to beam current using the ratios in Table 1. (The beam currents at corresponding spot sizes shown in Fig. 2 and Table 1 differ, because of such changes in instrument conditions.) If differences in beam current (Ib) and detector gain (G)
fully explained the effect of accelerating voltage on BSE noise, the noise-to-signal ratio would be inversely propor- tional to (GIb)0.5, for a given pixel dwell time. This was tested by plotting the product of the noise-to-signal ratio and
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