Outline of the ongoing discussion among the experts: Detection limit

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SEMI Standard procedure of carbon concentration measurement by IR

The detection limit in the SEMI Standard

In the SEMI Standard
3.2 The carbon level of the reference slice should be less than 2x1015 atomscm-3 (0.04 ppma) to minimize the comparative error at room temperature. The detection limit at cryogenic temperature (below 80 K) is about 0.01 ppma ( = 5x1014 atoms/cm3). Obtaining reference samples much below 0.01 ppma in carbon content may prove ---
(1)There is no value for the room temperature measurement
(2)There is no further explanation.
(3)There is no evidence or reference for the value.
Discussion: Definition:
(1) The term "detection limit" is equivalent with "limit of detection" and a definition of this term is contained in the SEMI Compilation of Terms. Originally this term was defined in SEMI F67 and F68.
Lowest concentration that can be detected by an instrument. LOD is typically defined as three times the standard deviation of the mean noise level.

(2)This shows that the detection limit in the SEMI Standard means the "instrumental detection limit."
(3)This is a general comment. There is no further explanation on the "detection limit" for the case of IR in the SEMI Standard. It is necessary to give the definition for IR.

Instrumental detection limit (IDL)

Definition by IUPAC (International Union of Chemists) in the Gold Book
The limit of detection, expressed as the concentration, cL, or the quantity, qL, is derived from the smallest measure, xL, that can be detected with reasonable certainty for a given analytical procedure. The value of xL is given by the equation
xL= x bi + k sbi
where x bi is the mean of the blank measures, sbi is the standard deviation of the blank measures, and k is a numerical factor chosen according to the confidence level desired.
Source: IUPAC Orange Book, 2nd ed., p. 5.
IUPAC - limit of detection (L03540)
Comments by Wikipedia:
In analytical chemistry, the detection limit, lower limit of detection, or LOD (limit of detection), often mistakenly confused with the analytical sensitivity, is the lowest quantity of a substance that can be distinguished from the absence of that substance (a blank value) with a stated confidence level (generally 99%)---
There are a number of concepts derived from the detection limit that are commonly used. These include the instrument detection limit (IDL), the method detection limit (MDL), the practical quantitation limit (PQL), and the limit of quantitation (LOQ). Even when the same terminology is used, there can be differences in the LOD according to nuances of what definition is used and what type of noise contributes to the measurement and calibration.
(1)IUPAC definition does not specify the "instrumental" detection limit
(2)It is for the general single measurement but not for the differential method
(1)Application to the differential infrared absorption spectroscopy (DIR)
DIR is not a single measurement but the subtraction between the two measurements. What is the "blank" in this case? The measurement of the two samples with equal concentration near expected DL and subtraction between the two measures may correspond to that.
(2)Example of IDL
Usually measurement is done 8 times. The standard deviation and the DL is calculated.
(i)For concentration above 1x1014/cm3:
The baseline between 590 and 619 cm-1 is recommended. The sample of 3x1014/cm3 was used. The standard deviation and the DL were calculated to be 3 and 8x1014/cm3, respectively.
(ii) For concentration above 1x1014/cm3:
The baseline between 590 and 619 cm-1 is recommended. The difference below the two samples was 3x1013/cm3 was used. The standard deviation and the DL were calculated to be 3 and 8x1013/cm3, respectively.
(iii) For concentration under 1x1014/cm3, the baseline is shortened to 600-610 cm-1. For this case, IDL below 1x1014/cm3 is obtained.
(iv) IDL is a word of statistics to exclude the under estimation of DL. There is the need for the reliable measurement of lower concentration than IDL.

Proposal: Spectral detection limit

Carbon concentration is obtained from the spectrum. The quality of the spectrum determine the successful measurement. As far as the interfering absorption bands are well defined, separated and smaller than the carbon peak, it is successful.
Therefore, the carbon peak height with equal height to the surrounding phonon absorption bands is the detection limit, the "spectral detection limit."
3x1013/cm3 is an example of the best SDL to now.

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