UltraLo-1800 Alpha Particle Counter
XIA LLC
Page 75
X.
Appendix
A.
Counter Efficiency
The UltraLo-1800's guard electrode, while critical for detecting sidewall events and eliminating
background counts, also causes the counter to detect alpha particles emitted from the sample with less
than 100% efficiency. Specifically, if an alpha particle is emitted from the sample and any portion of its
ionization track lies under the guard electrode, then that charge will be collected by the guard electrode,
producing an “alpha-like” output signal from the guard preamplifier. Meanwhile, the rest of the
ionization track is collected on the anode electrode, also producing an “alpha-like” output signal from
the anode preamplifier. Unfortunately, this pair of signals cannot be distinguished from a true sidewall
event (please refer to Figure II-6, where a sidewall α3 and α4 from the edge of the sample produce
similar output pulses). The event is therefore classified as a “sidewall” and rejected. (See Table II for
more information on trace classifications and resulting event classifications.)
The probability of ionization tracks crossing the anode-guard boundary clearly depends on both how
close the point of emission lies to the boundary and how long the track is. Right at the boundary fully
50% of emissions will cross under the guard, for example, while if a track is 3 cm long and it's emitted 4
cm from the boundary, its chance of crossing is clearly zero. Since track length varies with alpha particle
energy, counting efficiency is clearly energy-dependent. For a given energy (track length
𝐿
𝐸
) the
counting efficiency at each location within the sample area is then just that fraction
Ω
𝐸
of 2π solid angle
where
𝐿
𝐸
crosses the boundary – a straightforward geometric calculation. The counter’s total efficiency
〈Ω
𝐸
〉
at that energy is then the average of
Ω
𝐸
over the full sample area. We have carried out these
computations analytically and verified them with both Monte Carlo simulations and measurements with
a calibrated check source. The results are shown in the table below.
CounterMeasure then uses these efficiencies to correct the counter's output for “lost” alpha
particles. In principle this could be done in
two ways. The classical method would be
to wait until the measurement was
complete, bin the results by energy, and
then divide each bin result by the efficiency
at that energy to obtain a corrected
number of alpha particles. However, since
we want to be able to always display a
corrected emissivity value as the count
progresses, each time an alpha particle is
detected its energy E is measured and the
quantity
1 〈Ω
𝐸
〉
⁄
is
added
to
the
“corrected” number of alphas observed,
and used to compute the overall emissivity
from the sample.
E
α
(MeV)
Efficiency Corrections <Ω
E
>
Energy Range
<Avg> Full Config.
Wafer Config.
0 ≤ E < 1
0.5
1.0000
1.0000
1 ≤ E < 2
1.5
0.9816
0.9740
2 ≤ E < 3
2.5
0.9672
0.9542
3 ≤ E < 4
3.5
0.9497
0.9306
4 ≤ E < 5
4.5
0.9290
0.9035
5 ≤ E < 6
5.5
0.9052
0.8736
6 ≤ E < 7
6.5
0.8790
0.8424
7 ≤ E < 8
7.5
0.8505
0.8102
8 ≤ E < 9
8.5
0.8188
0.7769
9 ≤ E < 10
9.5
0.7876
0.7467
Table III: UltraLo-1800 Efficiency Corrections
