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SEMI MF1526-95 © SEMI 2004 9 ANNEXES (Mandatory I nformation) A1. RELATIONSHIP BETWEEN REPEAT ABILITY AND DETECTION LIMIT A1 .1 The consensus method to determine th e limit of detection, c L , in a photon spectr oscopy, …

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FIG. 3 Example BLANK (Except for Sulfur) Spectrum of Silicon Wafer Using TREX 610 Operated at 30 kV, 200
mA, 0.11°, 1000 s, Tungsten Target, LiF (200) Monochromator, W L-beta Line (9.67 keV)
SEMI MF1526-95 © SEMI 2004 9
ANNEXES
(Mandatory Information)
A1. RELATIONSHIP BETWEEN REPEATABILITY AND DETECTION LIMIT
A1.1 The consensus method to determine the limit of detection, c
L
, in a photon spectroscopy, when there is no
instrumental peak to subtract, is given as follows
13
:
c
L
= 3s
b
/S (A1.1)
where:
s
b
= the standard deviation of the BLANK measures, and
S = the sensitivity (net signal divided by atoms/cm
2
).
The numeral 3 in Eq. A1.1 is chosen so that a 99.6 % confidence level applies for a strictly one-sided Gaussian distribution; but
it is recognized that at low concentrations, non-Gaussian distributions are more likely.
A1.1.1 It is commonly assumed that the standard deviation of the BLANK measures, for short term measurements, is
given by Poisson statistics of the photons, and this leads to Eq A2.2 for the limit of detection which is commonly reported in
the technical literature.
c
L
= 3
()
areal density of ref
()
background counts
1/2
/
()
net signal (A1.2)
A1.1.2 This limit of detection includes the key assumption that the standard deviation of the BLANK measures is given
only by Poisson statistics of the X-ray photons, and that no other variability contribution is significant for this term. This
assumption may be valid only for short term estimation of the limit of detection.
A1.2 For long term estimation of the limit of detection, the standard deviation of the BLANK measures is expected to have
contributions from other variabilities than just the Poisson statistics, and therefore the long term estimation of the limit of
detection is expected to be larger than the short term limit of detection. Examples of other contributions to variability in the
BLANK measures may include, but not be limited to, the glancing angle calibration and X-ray beam divergence.
A2. COMPARING DATA SETS
A2.1 Introduction
A2.1.1 In qualifying a measurement system for operation, it can be useful to compare values ascribed to an artifact such as
a reference sample against those obtained for that artifact on a machine under test. This annex outlines a way in which the
multiple element measurement data can be used to monitor the effects of interferences that may arise from software
procedures and calculations in the instrument.
A2.1.2 A data set is that set of data used in computation of surface elemental contamination by TXRF.
A2.1.3 A referee wafer (artifact) is accompanied by its own data set (referee data set (RDS)), in which each data point is the
average of a number of repeated measurements. The artifact is measured on a machine under test and its RDS is compared
against the resultant measured sample data set. Differences in the data sets are computed. The parameter used to determine
agreement between the artifact and the system under test and the acceptable level of this agreement is to be agreed upon
between the using parties.
A2.2 Summary of Test Method
A2.2.1 Select a referee wafer of appropriate criteria, for which an RDS has been obtained.
A2.2.2 Measure the referee wafer on the machine under test to obtain a sample data set (SDS).
A2.2.3 Subtract the two to obtain a difference data set (DDS) as follows:
13 International Union of Pure and Applied Chemistry, Analytical Chemistry Division, “Nomenclature, symbols, units and their usage in spectrochemical
analysis—II, Data Interpretation,” Spectrochemica Acta, Vol 33, 1978, pp. 242–245.
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RDS SDS = DDS (A2.1)
where:
DDS = the differences between the measurements made on
the machine under test and the referee data set.
The DDS contains many values. The simplest metric that can be used to determine acceptability is the maximum difference,
the largest absolute value in the DDS. This represents the worst-case disagreement between the machine under test and the
referee data.
A2.2.4 Accept the machine as suitable for measurement if the maximum difference is less than a value that is agreed upon
between the parties to the test.
A2.2.5 More complex calculations may also be used, for example, a histogram of the (element-by-element) values of the
DDS along with statistical measures (mean, sigma, etc) may be compared. These measures can be compared to application-
specific limits or used to provide insight into the nature and source of the difference, or both.
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