1. Tracer Cert® Diffusion Tubes Technical Note 1 revised December 2014
Making ppb and sub-ppb water vapour standards using diffusion tubes for Quality Control of
measurements in Semiconductor Processing Industries
Dr. John M. Thompson
Tracer Measurement Systems Ltd., Institute of Research and Development,
Birmingham Research Park, Birmingham B15 2SQ, UK
&
Molecular Physics Group, School of Physics and Astronomy.
University of Birmingham, Birmingham, B15 2TH, UK
Introduction:
Measurements of trace water vapour concentrations in the low ppb v/v range are of major
importance to manufacturers of semiconductors, particularly as silicon wafer sizes have
been increased. The suppliers of special gases for semiconductor manufacturing have, as a
consequence, had to pay special attention to reducing trace water vapour concentrations in
the gases supplied to much lower levels as the needs of the semiconductor manufacturers
have progressed to more demanding specifications.
The methods of preparation of primary standards for trace water vapour concentration have
recently been reviewed under the project Euromet 1002: International comparability in
measurements of trace water vapour and published in a report by the UK NPL in June 2011
(ref. 1).
Various manufacturers offer commercial dew-point generators with low dew-point
capabilities down to -95ºC, for example, using volumetric mixing of dry and wet gases. Other
companies supply low emission rate permeation tubes and ovens. When the latter are
gravimetrically calibrated, they are useful secondary standards.
Recently, Thompson and Perry (JEM, 2009, ref. 2) published a new design for a range of
refillable, precision diffusion tubes that offer greater flexibility and ease of gravimetric
calibration. This paper describes the application of such tubes in making trace water vapour
standards in the ppb and sub-ppb range. These Tracer Cert® diffusion tubes are available
commercially, being manufactured by Tracer Measurement Systems Ltd. and distributed by
Eco Scientific Ltd. (e-mail: sales@eco-scientific.co.uk). An International Standard was first
published in 2005 about use of diffusion methods for trace gas calibration standards
preparation, ref 3: ISO 6145-8.
Experimental Methods
About 0.4ml distilled water was pipetted in a Tracer Cert® diffusion tube with the precision
bore tube part having a length of 6cm and a bore of 0.2cm. This was then weighed (using a
Cole Palmer Symmetry PA120 digital balance (120g x 0.1mg)) and then placed in an Eco
Scientific ES4050 thermostatic oven at 40ºC. The diffusion tube was weighed every few
days, over a period of 11 days, to make 4 weighings beyond the initial weighing, in order to
obtain sufficient weight loss measurements for a reasonable estimate to be made of the rate

2. of weight loss. For the calculation of the latter, the weight loss in mg versus the time in
minutes elapsed after the initial weighing was entered into the spreadsheet of Minitab®
statistical software v. 16 and various linear regressions of weight loss versus time were
done, as described below.
Results and Discussion
A useful lesson may be learned from a careful examination of the plots of the Ordinary Least
Squares Regressions (with and without intercepts) and the Robust Rank regression (with
intercept) of the 5 weight loss measurements in mg (measured to 0.1mg) versus time from
the start of the calibration experiment (see Figure 2, 3 and 4). The first datum point shows a
weight loss of zero mg, at the start of the experiment but the following 4 data points look to
be in more or less a straight line which does not go through the zero weight loss point at the
start time, demonstrating the importance of plotting sets of experimental data such as this.
The various regression analyses and associated plots are generated in Minitab version 16.
The Ordinary Least Squares and robust rank regressions with estimation of the intercept are
not forced through zero but, in these analyses, the zero weight loss point is a point of
influence and leverage exerting an effect on the slope estimate. The Ordinary Least Squares
regression without intercept forces the regression fit through zero. Neither version of the
Ordinary Least Squares regression fits is particularly robust and resistant, especially so with
data sets such as this in which the weights are measured to 0.1mg, as this has some
significant uncertainty at this level of subdivision.
In contrast, the hidden Rank Regression routine (rreg) in Minitab, developed by
Hettmansperger and McKean and based on the work of Jaekel, provides a more reliable,
distribution-free, robust and resistant estimate (refs 3, 4 and 5), as may be seen from the
plots in figure 4, in which there is a smaller intercept than for the Ordinary Least Squares
regression with an estimate of the intercept included.
The slope of the robust rank regression fit (0.00151) is usefully much closer to that of the
Ordinary Least Squares regression fit which was forced through zero (0.00176) than the
alternative Ordinary Least Squares regression fit with an intercept estimated (0.001395).
These regression slopes gives the required estimates of the rate of the water vapour weight
loss in mg per minute.
If the trace water vapour emission from the diffusion tube test, reported in this paper, was
fed into a dry gas flow of 250cm3
min-1
at 40ºC (about 313K), we would obtain a
concentration of 6.04 ng cm-3
or 0.336µmole/litre, corresponding to 8.6ppb(v/v). Were you to
use a Tracer Cert® diffusion with a precision bore tube section of 10cm length and 0.1mm
bore operated at 40ºC, water vapour emitted into a 250cm3
min-1
dry gas flow would give
1.29ppb(v/v). Look-up tables below show achievable emission rates and concentrations.
Conclusion
Using such diffusion tubes and gravimetrically calibrating them as described above to
reliably estimate of the rate of weight loss, could be valuable to those who are interested in
the calibration and quality management of measurements of ppb or sub-ppb range of trace
water vapour concentrations, especially for the manufacture and use of special gas mixtures

3. used in the semiconductor processing industries. It also facilitates the possibilities for further
reducing the trace water vapour concentrations in those industries.
References
1. P. J. Brewer, M. J. T. Milton. P. M. Harris, S. A. Bell, M. Stevens, G. Scace, H. Abe &
P. Mackrodt: “EURAMET 1002: International comparability in measurements of trace
water vapour” NPL Report AS 59, June 2011.
2. J. M. Thompson & D. B. Perry: “A new system of refillable and uniquely identifiable
diffusion tubes for dynamically generating VOC and SVOC standard atmospheres at
ppm and ppb concentrations for calibration of field and laboratory measurements”
Journal of Environmental Monitoring (2009) 11 1543-1544.
3. International Standards Organisation: ISO 6145-8 “Gas analysis – Preparation of
calibration gas mixtures using dynamic volumetric methods – Part 8: Diffusion
Method” First edition 2005-02-01
4. James C. Aubuchon: “Experimental Rank Regression (rreg) command, draft
documentation” Minitab Inc., March 1990.
5. Myles Hollander and Douglas A. Wolfe: “Nonparametric Statistical Methods” 1999,
2nd
. Edition, John Wiley and Sons Inc., pp 438-448 “General Multiple Linear
Regression 9.6. Asymptotically Distribution-free Rank-based Tests for General
Multiple Linear Regression (Jaeckel, Hettmansperger-McKean)”
6. Thomas P. Hettmansperger and Joseph W. McKean: “Robust Nonparametric
Statistical Methods” 2nd
Edition, 2011, Chapman and Hall/ CRC Press
Table 1: Emission rates for water vapour at 40ºC (313K) from different sizes of Tracer
Cert® diffusion tubes
Tracer tube code Precision Tube
bore, mm
Precision Tube
length, cm
Emission rate in
µg/min
CH 0.1 6 0.38
EH 0.1 10 0.28
AG 0.2 2 4.53
BG 0.2 4 2.27
CG 0.2 6 1.51
EG 0.2 10 0.91
CF 0.5 6 9.44
AE 1.0 2 113
BE 1.0 4 56.6
CE 1.0 6 37.8
EE 1.0 10 22.7
AC 2.0 2 453
BC 2.0 4 227
CC 2.0 6 151
EC 2.0 10 90.6
AA 4.0 2 1812
BA 4.0 4 906
CA 4.0 6 604

4. Table 2: Water vapour concentrations achievable with different Tracer Cert® diffusion
tubes at 40ºC (313K) and various carrier gas flow rates from 0.1l/min to 10l/min
Tracer tube
code
Carrier gas flow
l/min
Concentration in
ng l-1
Concentration
µmolar
Concentration in
ppb(v/v)
EH 0.1 3.8 0.21 5.5
0.25 1.5 0.084 2.2
0.5 0.76 0.042 1.1
1 0.38 0.021 0.55
2 0.19 0.011 0.28
5 0.076 0.0042 0.11
10 0.038 0.0021 0.055
EG 0.1 15.1 0.84 21.5
0.25 6.04 0.336 8.6
0.5 3.02 0.168 4.3
1 1.51 0.084 2.15
2 0.76 0.042 1.2
5 0.3 0.017 0.6
10 0.15 0.0084 0.22
EE 0.1 380 21 550
0.25 152 8.4 275
0.5 76 4.2 110
1 38 2.1 55
2 19 0.84 22.5
5 7.6 0.42 2.25
10 3.8 0.21 5.5
EC 0.1 1520 84 2200
0.25 608 33.6 880
0.5 304 16.8 440
1 152 8.4 220
2 76 4.2 110
5 30.4 1.68 44
10 15.2 0.84 22
AA 0.1 30400 1680 44000
0.25 12160 672 17600
0.5 6080 336 8800
1 3040 168 4400
2 1520 84 2200
5 608 33.6 880
10 304 16.8 440

5. Figure 1: Three typical Tracer Cert® diffusion tubes, the ones in the photograph have precision bore tube
section of lengths of 2cm, 4cm and 8cm with bore diameters of 1mm.
Figure 2: The Ordinary Least Squares regression (with no intercept) of the weight loss data in mg versus time
elapsed in minutes from the initial weighing using Minitab statistical software v16.

6. Figure 3: Plot of the weight loss data using Ordinary Least Squares regression with an estimate of the
intercept

7. Figure 4: Plot of the Robust Rank regression of the weight loss data