EURAMET.EM-S44
“Comparison for Ultra-low DC Current Sources”
Draft B Report
Enis TURHAN
TÜBİTAK Ulusal Metroloji Enstitüsü (UME)
24/05/2022
0
Contents
1.
Introduction .................................................................................................................................3
2.
Participants of the Comparison ...................................................................................................4
2.1. Participants .................................................................................................................................4
2.2. Pilot Institute ...............................................................................................................................5
3.
Organisation of the Comparison .................................................................................................5
3.1. The time schedule ......................................................................................................................5
3.2. Unexpected events .....................................................................................................................5
4.
Travelling Standard.....................................................................................................................6
5.
Quantities to be Measured and Conditions of Measurements .....................................................6
6.
Measurement Instructions ...........................................................................................................7
7.
Temperature and humidity during the comparison measurements ..............................................8
8.
Calibration methods used by the participants ..............................................................................9
9.
Measurement Results of Participants........................................................................................11
9.1. Measurements of the Participants .............................................................................................11
9.2. Behaviour of the Travelling Standard ........................................................................................18
10. Analysis of Measurement Results of the Participants ................................................................24
10.1.
Method of analysis.............................................................................................................25
10.1.1.
Method of determining the reference values and the degrees of equivalence ................25
10.1.2.
Modification due to linear drift of the transfer standard ...................................................27
10.2.
Measurement Results........................................................................................................34
11. Withdrawals or Change of Results ............................................................................................64
12. Summary and Conclusions .......................................................................................................64
13. References ...............................................................................................................................65
Appendix A: Results of the participants in chronological order .........................................................66
Appendix B: Uncertainty Budgets of the participants........................................................................73
Appendix C: Technical Protocol .........................................................................................................1
1
List of Tables
Table 1. List of participating laboratories ...........................................................................................4
Table 2. Circulation Time Schedule ...................................................................................................5
Table 3. Measurement quantity & points ...........................................................................................7
Table 4. Temperature and Humidity Values Declared by the Participants .........................................8
Table 5. Fit parameters of the drift of the transfer instrument and the corresponding uncertainties .27
Table 6. Results for 95 pA, positive current direction .......................................................................35
Table 7. Results for 95 pA, negative current direction .....................................................................37
Table 8. Results for 95 pA, mean of both current directions ............................................................39
Table 9. Results for 9.5 pA, positive current direction ......................................................................41
Table 10. Results for 9.5 pA, negative current direction ..................................................................43
Table 11. Results for 9.5 pA, mean of both current directions .........................................................45
Table 12. Results for 0.95 pA, positive current direction ..................................................................47
Table 13. Results for 0.95 pA, negative current direction ................................................................49
Table 14. Results for 0.95 pA, mean of both current directions* ......................................................51
Table 15. Results for 95 fA, positive current direction ......................................................................52
Table 16. Results for 95 fA, negative current direction ....................................................................54
Table 17. Results for 95 fA, mean of both current directions* ..........................................................56
Table 18. Results for 9.5 fA, positive current direction .....................................................................58
Table 19. Results for 9.5 fA, negative current direction ...................................................................60
Table 20. Results for 9.5 fA, mean of both current directions* .........................................................62
2
1. Introduction
As supplementary comparison on the subject low DC current measurements, EURAMET.EM-S24
(EUROMET project 830 “Comparison of small current sources”), was carried out from 2005 to 2009.
The objective of the present comparison is to provide technical evidence to support the CMCs
entries of those participants who did not participate in the EURAMET.EM-S24, as well as those of
participants that did participate in EURAMET.EM-S24 but have since improved their measurement
capability. The comparison was performed at ± 9.5 fA, ± 95 fA, ± 0.95 pA, ± 9.5 pA, ± 95 pA.
A commercial electrometer Keithley 6430 was used as travelling standard.
TÜBİTAK UME acted as the pilot laboratory and also provided the travelling standard. TÜBİTAK
UME was responsible for monitoring the performance of the travelling standard during the circulation
and for the evaluation and reporting of the comparison results.
The project number given by EURAMET was “1381”. Subsequently the comparison name was
changed to EURAMET.EM-S44.
After the announcement of the comparison, 7 NMIs applied to take part. All of the participant
institutes are members of EURAMET.
The comparison was conducted in accordance with the CCEM Guidelines for Planning, Organizing,
Conducting and Reporting Key, Supplementary and Pilot Comparisons [1] and the Technical
Protocol which was prepared by the TÜBİTAK UME and approved by the participants is given in
Appendix C. The evaluation of the measurement results was performed in accordance with
guidelines for uncertainty evaluation [2] and the evaluation of comparison data [3,4].
3
2. Participants of the Comparison
2.1. Participants
List of participating laboratories is given in Table 1.
Table 1. List of participating laboratories
Acronym of
Institute
LNE
BFKH
NSAI NML
IPQ
RISE
METAS
TÜBİTAK UME
Country
Contact Person
Shipping Address
FRANCE
Daniela Istrate
Daniela.Istrate@lne.fr
Tel : +33 1 30 69 10 00
Fax : +33 1 30 69 12 34
Laboratoire national de métrologie et
d'essais 29
Avenue Roger Hennequin - 78197
Trappes cedex, FRANCE
HUNGARY
Tibor Németh
nemeth.tibor@bfkh.gov.hu
Tel.: +36 1 4585-897
Fax: +36 1 4585-823
Government Office of the Capital
City Budapest
Metrological and Technical
Supervisory Department,
Section of Electrical, Thermophysical
and Optical Measurements
37-39 Németvölgyi Street
Budapest, H 1124
HUNGARY
IRELAND
Oliver Power
Oliver.Power@nsai.ie
Tel.: +353 1 808 2610
Fax: +353 1 808 2603
NSAI National Metrology Laboratory
Griffith Avenue Extension
Glasnevin
Dublin 11
IRELAND
PORTUGAL
Luis Ribeiro
LRibeiro@ipq.pt
Tel.:+351 212948161
IPQ – Instituto Português da
Qualidade
Rua António Gião, 2
2829-513 Caparica
PORTUGAL
SWEDEN
Tobias Bergsten
tobias.bergsten@ri.se
Tel.: +46 (0)10 516 5116
RISE Research Institutes of Sweden
Measurement Science and
TechnologyBox 857,
SE-501 15 Borås,
SWEDEN
SWITZERLAND
David Corminboeuf
david.corminboeuf@metas.ch
Tel.: +41 58 387 06 42
Fax: +41 58 387 02 10
Federal Institute of Metrology
METAS
Lindenweg 50, 3003 Bern-Wabern,
SWITZERLAND
TURKEY
Enis TURHAN
enis.turhan@tubitak.gov.tr
Tel.: +90 262 679 50 00
TÜBİTAK Ulusal Metroloji Enstitüsü
(UME)
TÜBİTAK Gebze Yerleşkesi
Barış Mah. Dr. Zeki Acar Cad. No:1
41470 Gebze-Kocaeli, TURKEY
4
2.2. Pilot Institute
This comparison was piloted by TÜBİTAK UME. Pilot laboratory was responsible for preparing the
measurement instructions, controlling the stability of the transfer standard, calculating the results
and preparing the comparison report.
3. Organisation of the Comparison
3.1. The time schedule
The time schedule for the comparison is given in the Table 2. Circulation of the travelling standard
started in March 2015 and comparison measurements were completed in September 2016. The
circulation of travelling standard was organized in loops of not more than 3 institutes in order to
monitor the performance of the travelling standard. Each participating institute covered the costs of
customs clearance, and shipment to the next institute.
Table 2. Circulation Time Schedule
Acronym of
Institute
Country
Starting Date
Time for
Measurement and
Transportation
TÜBİTAK UME
Turkey
01.03.2018
6 weeks
LNE
France
17.04.2018
7 weeks
NSAI
Ireland
05.06.2018
4 weeks
TÜBİTAK UME
Turkey
02.07.2018
10 weeks
METAS
Switzerland
14.09.2018
5 weeks
HU-BFKH
Hungary
17.10.2018
4 weeks
RISE
Sweden
17.11.2018
6 weeks
TÜBİTAK UME
Turkey
26.12.2018
20 weeks
IPQ
Portugal
22.05.2019
7 weeks
TÜBİTAK UME
Turkey
10.07.2019
21 weeks
TÜBİTAK UME
Turkey
21.04.2020
14 weeks
3.2. Unexpected events
During the course of the comparison, some delays occurred in the planned schedule due to severe
customs and transport delays. No damage was reported to the travelling standard during the
comparison.
Because of the Covid-19 pandemic conditions, some delays in customs and in sending the
participants reports, the duration of the circulation was longer than planned.
5
4. Travelling Standard
The travelling standard, supplied by TÜBİTAK UME, was an electrometer, Keithley 6430, serial
number 4081508 (Figure 1).
The travelling standard has very special input connectors, therefore it was accompanied by
appropriate adapters with appropriate BNC connectors.
The travelling standard was supplied by TÜBİTAK UME. The standard was chosen for its high
accuracy and stability in time.
Figure 1. Travelling standard is Keithley 6430 Electrometer with the serial number of 4081508
5. Quantities to be Measured and Conditions of Measurements
The measurements were carried out by calibrating the transfer instrument, i.e. by supplying a DC
current specified by the participant’s current source and recording the instruments reading. The
measurands were then the calibration factors of the transfer instruments, defined as the ratio of
reading of the transfer instrument to the supplied current.
The nominal values of the eight measuring points were +10 fA, -10 fA , +100 fA, -100 fA, +1 pA,
-1 pA, +10 pA, -10 pA, + 100 pA, and -100 pA. In order to take full advantage of the transfer
instruments resolution and to avoid internal range switching the calibration points must be slightly
below the nominal values. Therefore, the calibration points were chosen to be 0.95 times the
nominal values, e. g. 95 fA, 0.95 pA.
The quantities to be measured are given in Table 5.
6
Table 3. Measurement quantity & points
Quantity
Nominal Value
Current Measurement
Range
+9.5 fA
-9.5 fA
+95 fA
1 pA
-95 fA
+0.95 pA
DC Current
-0.95 pA
+9.5 pA
10 pA
-9.5 pA
+95 pA
100 pA
-95 pA
The main parameter was DC current. In addition, the quantities given below were measured and
recorded;
 Ambient temperature
 Ambient humidity
 Atmospheric pressure
The participants were not obliged to measure all of the values. The participants had an option to
choose the measurement values in accordance with their measurement capability.
No correction was applied for the ambient temperature, relative humidity and atmospheric pressure.
The measurements were carried out at a temperature of (23 ± 1) °C and at a relative humidity of (45
± 15) %rh.
6. Measurement Instructions
Before the measurements, the travelling standard was turned on and allowed to stabilize for at least
one day in the laboratory.
The instrument had to be operated remotely. A GPIB-USB adapter was provided with the
instrument. The user manual was not supplied with the device. The user manual of the device is
open source reachable from the manufacturer’s website.
7
The transfer instrument had considerable time constants. To take this into account, a settling time of
15-20 s after each current change had to be allowed. Instructions and specific commands for the
instrument were given in the Technical Protocol in Appendix C.
7. Temperature and humidity during the comparison measurements
Table 4. Temperature and Humidity Values Declared by the Participants
23.0 ± 0.5
Relative
Humidity
(%rh)
45 ± 5
Atmospheric
pressure
(mbar)
1015 ± 15
HUNGARY
22.64 ± 0.45
43.8 ± 6.2
1000.6 ± 0.9
NSAI NML
IRELAND
23 ± 1
40 ± 5
1012 ± 6
IPQ
PORTUGAL
23 ± 1
53 ± 10
1006 ± 4
RISE
SWEDEN
23 ± 1
45 ± 10
1020 ± 10
METAS
SWITZERLAND
22.9 ± 0.5
48 ± 5
962 ± 11
TÜBİTAK UME
TURKEY
23 ± 1
45 ± 15
1000 ± 15
Temperature
Acronym of
Institute
Country
LNE
FRANCE
HU-BFKH
(ºC)
8
8. Calibration methods used by the participants
Two different calibrating methods were used by the participants, in the comparison.
8.1. Generating the calibrating current by charging/discharging a capacitor
The calibrating current I is generated by charging or discharging a gas-filled capacitor C with a
linearly increasing or decreasing voltage of slope dV/dt. The calibrating current is then I=C·dV/dt.
Thus, it is traced back to the volt, the second and the farad. Typically, a trapezoidal voltage pattern
symmetrical to zero voltage is used which allows the elimination of linear drifts and the influence of
leakage currents across the capacitor. This is discussed in more detail in [5].
Figure 2. Schematic calibration set-up for using the capacitor-charging method
This method was used by all of the participants.
8.2. Generating the calibrating current by a voltage source and a resistor
The calibrating current I is generated by a voltage source V (e.g. a DC calibrator) and a resistor R. It
is then I = V/R. Thus, the current is traced back to the volt and the ohm.
9
Figure 3. Schematic calibration set-up for using the voltage-resistor method
This method was used by TUBİTAK UME and LNE.
8.3. Comparison of the transfer instruments with a traceable picoammeter
In this method used exclusively by LNE, the calibrating current is generated by a current source
consisting of a voltage source and a resistor, but, in contrast to the method described above, the
generated current is not directly traced back to the volt and the ohm. Instead, in a second step, the
current source is calibrated by a traceable current measuring set-up. This method is described in
more detail in Section 9.1.2.
10
9. Measurement Results of Participants
9.1. Measurements of the Participants
The measurement set-up used by each participant laboratory is described in this section in
chronological order. Descriptions of the traceability chains are not given here.
9.1.1. Measurements of TUBITAK UME
The measurement results for 95 pA and 9.5 pA currents were performed using Ohm’s Law principle.
95 pA current value was generated by applying 0.1 V voltage over 1 GΩ standard resistor. 9.5 pA
current value was generated by applying 0.1 V voltage over 10 GΩ standard resistor. These
currents were measured with transfer instrument and ratio was determined.
For other current values (0.95 pA, 95 fA and 9.5 fA) a capacitor charging method was used. The
voltage ramp was generated by a commercial DAQ card (NI-USB 4431). The ramp slope was
measured by an Agilent 3458A multimeter. The triggering was performed by a precision time base
generated from a microprocessor board and measured regularly with a calibrated frequency counter.
The capacitors used to generate the current were of type HP 16382A (10pF), 16383A (100 pF) and
16384A (1000 pF). These capacitors were placed in a temperature controlled (±5 mK stability)
isolated box. The capacitors were measured regularly using a calibrated AH2700A capacitance
bridge.
Measurements were performed in temperature and humidity controlled laboratory environment.
9.1.2. Measurements of LNE
For each nominal value, the result has been obtained as the weighted mean value of several
methods. Two methods were used: (1) Voltage-resistor method; (2) Sub-Femtoamp Current source
as transfer standard that was calibrated by the primary standard, which is the LNE integration
bridge. However, only the method (2) was used for 95 pA measurements.
The current supplied by the low current source is at first measured by the device to be calibrated,
the travelling standard. In the second step, the current source is calibrated by means of the
integration bridge.
(1) Voltage-resistor method
The DC low current is generated by a voltage source, V (a stable DC voltage generator) and a high
value resistor, R, which resistance is chosen to obtain the desired range of current (Figure 4).
I = V/R. The DC voltage generator was calibrated in the LNE laboratory using DC voltage reference
standard. The high value resistors were calibrated by means of the LNE integration bridge.
11
Figure 4. Schematic calibration set-up for voltage-resistor method
(2) Sub-Femtoamp Current source as transfer standard and LNE integration bridge as primary
standard
In the second method a transfer technique is used to calibrate the current meter. The output of a
stable, low current source is measured in turn by a reference ammeter and ammeter under test. The
reference ammeter is described in detail in [6] and [7]. The low current is generated by the LNE SubFemtoamp source type Keithley 6430 with the SN° 1078229 and its preamplifier SN° 1064638. This
current source was used to calibrate the travelling standard and immediately after, the LNE SubFemtoamp source was calibrated at the same current using the integration bridge. This home-made
set-up is composed of a group of standard air capacitors connected to an operational amplifier in an
integrating configuration. The current, “𝐼𝑥 = −𝐶 ∙ 𝑑𝑈/𝑑𝑡” is traced back to the volt, the farad and the
second.
Figure 5. Measuring principle of integration bridge
12
9.1.3. Measurements of NSAI
The reference currents used to determine the calibration factor of the electrometer were generated
using the capacitance charging method. A voltage ramp generator was used to charge and
discharge a gas filled capacitor thus producing a constant current of value “I=C·dV/dt”, where C is
the capacitance of the capacitor at DC and “dV/dt” is the slope of the voltage ramp.
Each cycle of the ramp generator consisted of positive and negative sections of duration
approximately 105 s separated by constant voltage sections of duration approximately 100 s. The
peak-to-peak voltage of the ramp signal was 10 V thereby giving a ramp slope of approximately 95
mV/s. A ramp with slope 0.95 V/s could also be generated using a X10 amplifier. The capacitors
used ranged in value from 0.01 to 1000 pF and were either sealed gas filled capacitors (GenRad
1404, ESI SC1000) or air dielectric capacitors (Gen Rad 1403, HP 1638*A). The capacitance of the
capacitor used to generate the reference current was measured at 1 kHz both before and after a
measurement run using a capacitance meter (Andeen Hagerling 2700A). Both the voltage of the
ramp signal and the reading of the electrometer were sampled at 1 second intervals. The ramp
voltage was measured using a digital voltmeter (HP 3458A) which was triggered by a function
generator. The period of the function generator was measured by a frequency counter locked to the
laboratory’s reference frequency standard. The same signal was used to trigger the electrometer. A
typical measurement consisted of ten ramp cycles.
During the measurements, the 6430 Remote Pre-Amp was laid flat on the bench with the face
showing the model number upwards. The 3-Lug Triax(m)-BNC(m) cable, supplied by the pilot
laboratory, was used to connect the capacitor to the pre-amplifier. In this configuration, there is no
connection to the inner screen of the triaxial connector.
All the sampled data was recorded, but for the data analysis only the data from the second half of
each section of the ramp cycle was retained. This was to allow for settling of the electrometer
reading. The mean values of the reference current and the corresponding electrometer reading were
calculated for each section of the ramp. The values from the constant voltage sections of the ramp
were used to correct for zero offsets. The calibration factor of the electrometer was calculated from
the formula:
𝑸=
−(𝑿 − 𝑿𝟎 )
(𝑰𝑿 − 𝑰𝟎 )
(1)
where 𝑿 and 𝑿𝟎 are the electrometer readings corresponding to the nominal input test current 𝑰𝑿
and nominal zero input current 𝑰𝒐 and the negative sign is included since currents flowing into the
positive terminal of the electrometer are displayed as negative values.
13
9.1.4. Measurements of METAS
A reference current, generated across a standard capacitor CS driven by a voltage ramp, is applied
to the unit under test (UUT) as shown in Figure 6.
Figure 6. Principle of the current source
The current applied to the UUT is therefore: IApplied = CS·(dV/dt)
The ramp voltage is measured by a high resolution voltmeter and the slope of the ramp is calculated
by triggering the voltmeter at precisely timed intervals. The slope is controlled with a PID
compensator to the desired value. For each measurement point, 20 rising ramps and 20 falling
ramps are applied to CS. Only measurement points taken symmetrically about ground potential are
used to form the reported averages. Hence we assume that the effect of the parasitic conductance
of CS is compensated for. Each ramp is preceded and followed by a period of time where the ramp
generator output is held constant at two values symmetrical with respect to ground level. The current
measurements in these halt intervals are used to compensate current offsets as discussed for
instance in [5].
14
9.1.5. Measurements of HU-BFKH
Our method and instruments used in this project: In this project we used a PAM2012 (PicoAmMeter)
instrument, which is a complex appliance for aide the work with open air ionization chambers. It
contains a high voltage source, an environmental monitor to log the temperature, the air pressure
and the humidity, and a sensitive DC current integrator with a set of capacitors. It works under
computer control and its program handles the chamber set properties, applies chamber sensitivity
corrections computed from the measured pressure and temperature, it supplies the chamber with
high voltage. In this project we used only the ambient monitor and the sensitive current integrator.
PAM2012 was used only as linear extrapolation device for the step down procedure. We applied 2
of the capacitors, 1100 pF and 100 pF nominal value. The PAM2012 and the program provide wide
range of time period and wide range of voltage scale to measure the charge. Both of them are
implemented by digital methods.
The first step
The input of the current integrator is a virtual earth point of classical current integrator built by an
operational amplifier. A calibrated 1 GΩ resistor was connected between the voltage output of
Fluke5700 and the input of the current integrator. The common low point of both instrument was
connected together and grounded. Because the input voltage of the integrator is nearby zero, the
voltage on the resistor is nominally equal to the output voltage of the calibrator. At 100 mV level it
produces 100 pA current. This current value was used to calibrate the 1100 pF nominal capacitor of
the current integrator. The measurement at 95 pA level based on this calibration later.
The second step
A current value of 30 pA was used to calibrate the 100 pF capacitor. The current was produced by
the travelling standard but the accurate value was determined by the previously calibrated 1100 pF,
with long time (150 s) integration. After that the 100 pF value was calibrated by shorter time (13 s)
integration of this known current. Later all the lower current values were measured based on this
capacitor.
The input operational amplifier has input bias current of 7 fA which was measured frequently, by left
open the input. In these cases we saw that the input BNC connector has some triboelectric
behaviour. Significant but decreasing current was present for a quarter of an hour after unplugging
the BNC. To avoid this effect, we had to insert a delay between changing of connection and start of
data reading. The value of the input bias current (7 fA) was applied as correction in each case and
its standard deviation (0.5 fA) was taken account as uncertainty contributor. The input voltage was
assumed as zero, but of course, it is not exact. This property was significant only at the first step, at
the calibration of 1100pF range with Fluke5700, since the used circuit arrangement was not really a
current source. To eliminate the effect of the offset voltage we have inserted the measurement with
zero output voltage of the Fluke5700. In this case, the measured current was the offset voltage
divided by 1 GΩ plus the input bias current. Later, when the source was the travelling standard, the
offset voltage was not taken into account because the source could produce the necessary voltage.
15
9.1.6. Measurements of RISE
The measurement was performed as described in [8], using an arbitrary waveform generator (AWG)
to generate a voltage ramp, charging a capacitor at a constant current. The charging current was
defined by the relation
𝐼=𝐶
𝑑𝑉
𝑑𝑡
where, I is the charging current, C is the capacitance and
(2)
𝑑𝑉
𝑑𝑡
is the slope of the voltage ramp.
The capacitance was determined by comparing a charging current through a capacitor with the
same current through two calibrated resistors of 10 MΩ and 100 MΩ, using a source-meter as a
transfer standard. This comparison was done at 4 nA, using a 4 nF capacitor. Then the 1 nF
capacitor was compared to the 4 nF one at 1 nA, and finally 1 nF was compared to 10 pF at 10 pA.
Result: 1 nF (-18 ± 21 ppm); 10 pF (-336 ± 38 ppm).
The voltage ramp was measured with a calibrated digital multimeter, triggered from an AWG. The
AWG reference clock was controlled by a 10 MHz signal from the time lab at RISE with insignificant
uncertainty.
The charging current was measured by the travelling standard and then divided by I to give the ratio
Q:
𝑄=
𝐼𝑡𝑠
𝑑𝑉
𝐶
𝑑𝑡
(3)
where, 𝐼𝑡𝑠 is the indicated value of the travelling standard.
16
9.1.7. Measurements of IPQ
The measurements were carried out by supplying the specified DC current, through the setup
implemented at IPQ, based on the method of charging a capacitor using a voltage source changing
linearly with time at a rate “dV / dt”. In that way, a constant current is generated according to
“I = C · dV / dt”, with the value of the current being traced back to the units of capacitance, voltage
and time. According to the technical protocol, the measurand should be the calibration factor Q that,
in this setup, follows the simplified model:
(4)
with,
I
kI
C
dV
kV
dt
: Representing the readout of the instrument;
: A constant value of 0 associated to its limited resolution;
: The value of the standard capacitor used for the current source;
: The voltage step to charge the capacitor;
: A constant value of 0 associated to its limited resolution;
: The charging time
17
9.2. Behaviour of the Travelling Standard
TUBITAK UME monitored the behaviour of the transfer instrument in this comparison. The drift of
the transfer instrument was determined by using individual measurements of TÜBİTAK UME,
performed in different times starting from March 2018 up to July 2020, which can be seen in Table 2.
The measurements performed by TUBITAK UME to monitor drift behaviour of the transfer
instrument reflect both the behaviour of the travelling instruments as well as the behaviour of
TUBITAK UME’s measurement set-up. However, it is reasonable to assume that the systematic
errors of the TUBITAK UME’s measurement set-up are the same for the drift measurements of each
measurement point.
The following graphs, which represent the drift behaviour of Keithley 6430 transfer instrument, are
based on the TUBITAK UME’s measurements.
A linear drift was observed at ±95 pA, ±9.5 pA and ±0.95 pA values. The drift values can be seen in
Table 5 in Section 10.1.2. For the values of ±95 fA and ±0.95 fA, a linear drift was not detectable
since the drift behaviour is hidden in TUBITAK UME’s measurements with comparatively larger
measurement uncertainties. In addition, the measurement uncertainties of the participants made the
effect of any drift correction negligible for ± 95 fA and ± 9.5 fA current values.
18
Q(+)
+95 pA
1,00042
1,00040
1,00038
1,00036
1,00034
1,00032
1,00030
1,00028
Figure 7. Drift of travelling standard at +95 pA,
Q(-)
-95 pA
1,00038
1,00036
1,00034
1,00032
1,00030
1,00028
1,00026
1,00024
Figure 8. Drift of travelling standard at -95 pA
19
Q(+)
+9.5 pA
1,00140
1,00130
1,00120
1,00110
1,00100
1,00090
1,00080
1,00070
Figure 9. Drift of travelling standard at +9.5 pA
Q(-)
-9.5 pA
1,00140
1,00130
1,00120
1,00110
1,00100
1,00090
1,00080
1,00070
Figure 10. Drift of travelling standard at -9.5 pA
20
Q(+)
+0.95 pA
1,0024
1,0020
1,0016
1,0012
1,0008
1,0004
1,0000
Figure 11. Drift of travelling standard at +0.95 pA
Q(-)
-0.95 pA
1,0024
1,0020
1,0016
1,0012
1,0008
1,0004
1,0000
Figure 12. Drift of travelling standard at -0.95 pA
21
Q(+)
+95 fA
1,00600
1,00400
1,00200
1,00000
0,99800
0,99600
Figure 13. Drift of travelling standard at +95 fA
Q(-)
-95 fA
1,00600
1,00400
1,00200
1,00000
0,99800
0,99600
Figure 14. Drift of travelling standard at -95 fA
22
Q(+)
+9.5 fA
1,0600
1,0400
1,0200
1,0000
0,9800
0,9600
0,9400
Figure 15. Drift of travelling standard at +9.5 fA
Q(-)
-9.5 fA
1,0600
1,0400
1,0200
1,0000
0,9800
0,9600
0,9400
Figure 16. Drift of travelling standard at -95 fA
23
10. Analysis of Measurement Results of the Participants
The measurement results reported by the participants (see Appendix A) mainly contain the
calibration factors Q+ (defined as the ratio of the transfer instrument’s reading / supplied current) for
a current flowing into the transfer instrument and Q- for a current flowing out of the transfer
instrument, accompanied by their standard uncertainties u(Q+) and u(Q-) and their effective degrees
of freedom.
Some participants reported the measurement data sets along with standard uncertainties and
degrees of freedom values. The pilot laboratory calculated coverage factors k corresponding to 95%
confidence level and the corresponding expanded uncertainties U(Q+) and U(Q-).
Some participants reported the measurement data sets along with expanded uncertainties. The
measurements results of the participants and their related uncertainty values are given in the tables
of Appendix A.
In order to see zero offset effects related to the transfer instrument, the mean value of Q+ and Qvalues, which is Qmean = ([Q+] + [Q-])/2, was also declared. Besides, the mean value is also declared
in EURAMET.EM-S24. However, we did not see a zero offset problem as seen in EURAMET.EMS24 for PTW Unidos E device.
Since typically the sources for type B uncertainties are the same for Q+ and Q-, a high degree of
correlation can be assumed and the uncertainty of Qmean is calculated by U(Qmean) = (U(Q+)+U(Q-))/2.
In reality, the correlation is not perfect and, therefore, this formula may overestimate the correct
uncertainties, especially at the lower current values where the type A uncertainty components are
significant.
24
10.1. Method of analysis
The aim of the analysis is to establish
i)
Comparison reference values (Qref) of each current value for positive direction (Q+),
negative direction (Q-), and the mean of both current directions (Qmean).
ii)
A corresponding degree of equivalence (di, U(di)) with di = Qi – Qref and U(di) being the
expanded uncertainty of di for a coverage of 95% (see [3,4] Cox) for each result of a
participant
In general, the data sets were not completely consistent. In addition, the measurement results are
uncorrelated. Therefore, the method described by Cox in [4] is used to determine the reference
values Qref and the largest consistent data sets. This method is described briefly in Section 10.1.1.
Furthermore, a modification was necessary in order to take into account the drift behaviour of the
Keithley 6430, which is described in Section 9.2.
10.1.1. Method of determining the reference values and the degrees of equivalence
The Comparison Reference Values (𝑄𝑟𝑒𝑓 ) are calculated for each measurement point at positive
current direction, negative current direction, and the mean of both current directions as a weighted
mean of the largest consistent subset of Qi (i = 1….N) following the procedure described in more
detail in [3,4]:
For each result Qi, a function ei (Qref) is defined as
(𝑄𝑖 − 𝑄𝑟𝑒𝑓 )2
𝑒𝑖 (𝑄𝑟𝑒𝑓 ) =
𝑢2 (𝑄𝑖 )
(5)
where Qref is still unknown. The sum Fr over these functions is again a function of Qref f
𝑟
(6)
𝐹𝑟 (𝑄𝑟𝑒𝑓 ) = ∑ 𝑒𝑖 (𝑄𝑟𝑒𝑓 )
𝑖=1
25
Qref is then determined by numerically searching the minimum of Fr(Qref) using the method
described in Section 5.2 of [4]. In a first step, all results are taken into account, i.e. r = N.
The results are regarded as consistent and the value for Qref is accepted if
𝐹𝑟 (𝑄𝑟𝑒𝑓 ) ≤ 𝝌𝟐(r – 1; 0.05)
(7)
2
Where 𝜒𝑣,𝛼
denotes the 100α percentage point of the chi-squared distribution with ν degrees of
freedom. α was taken here as 0.05.
If the results are not consistent, r is decremented by one, i.e. N-r results with the largest values of 𝑒𝑖
are discarded from calculating Qref and the procedure is restarted at Equation (8). This cycle is
repeated until consistency is achieved. For a more detailed description of the method of selecting
the discarded results in [4].
After the largest consistent subset is determined Qref is calculated by using undiscarded results of
participants with the following equation
𝑄𝑖
𝑢(𝑄𝑖 )2
=
1
∑r𝑖=1
𝑢(𝑄𝑖 )2
∑𝑟𝑖=1
𝑄𝑟𝑒𝑓
(8)
The uncertainty of comparison reference values 𝑢(𝑄𝑟𝑒𝑓 ) is calculated according to
𝑟
1
1
=∑ 2
2
𝑢 (𝑄𝑟𝑒𝑓 )
𝑢 (𝑄𝑖 )
(9)
𝑖=1
The expanded uncertainty of the Comparison Reference Values (𝑄𝑟𝑒𝑓 ) was calculated by:
𝑈(𝑄𝑟𝑒𝑓 ) = 2 × 𝑢(𝑄𝑟𝑒𝑓 )
(10)
26
10.1.2. Modification due to linear drift of the transfer standard
As mentioned in Section 9.2, the Keithley 6430 showed an obvious drift behaviour at currents of
0.95 pA, 9.5 pA and 95 pA. This was taken into account by assuming a linear dependence of the
transfer instrument with time.
The drift of the transfer instrument was modelled using a linear fit, given as in Equation (11):
𝑄 = 𝑄0 + 𝑚 × (𝑡𝑖 − 𝑡0 )
(11)
Where,
𝑄
(10-6 )
The measurement result given by linear fit on date 𝑡
𝑄0
(10-6 )
The average measurement result of the TÜBİTAK UME measurements
𝑡𝑖
( days )
A given measurement date
𝑡0
( days )
The mean measurement date of the first and the last TÜBİTAK UME
measurements, which is 30.04.2019
𝑚
(10-6 /day )
The drift of the Q value for the travelling standard per day
The fit parameters of the drift of the transfer instrument and the corresponding standard
uncertainties (𝑘 = 1) are given in Table 5.
Table 5. Fit parameters of the drift of the transfer instrument and the corresponding uncertainties
Measurement
Point
𝒕𝟎
𝑸𝟎 *
𝒖(𝑸𝟎 )
𝒎
(10 /day)
𝒖(𝒎)
(10-6/day)
𝒄𝒐𝒗(𝑸𝟎 , 𝒎)
(10-6/day)
+95 pA
30.04.2019
1.000352
0.000508
0.103
0.012
-5.91·10-6
-95 pA
30.04.2019
1.000313
0.000691
0.098
0.016
-10.96·10-6
+9.5 pA
30.04.2019
1.00110
0.00162
0.303
0.037
-59.9·10-6
-9.5 pA
30.04.2019
1.000970
0.000863
0.203
0.020
-17.05·10-6
+0.95 pA
30.04.2019
1.00129
0.00483
0.523
0.111
-5.34·10-4
-0.95 pA
30.04.2019
1.00117
0.00377
0.552
0.086
-3.25·10-4
-6
*: Q0 values in the Table 5 are the measurement values of TUBITAK UME on the mean date, which
were only used to determine drift values of the transfer instrument. Since the pilot laboratory is
responsible only for determining the drift values these Q0 values were not used in the calculations.
27
The measurement results were required to be reported as the ratio of the travelling standard in
proper range, calculated by;
𝑄𝑖 =
Reading of the Transfer Instrument
Supplied Current
(12)
Each participant results (𝑄𝑖 ) were corrected to get the corrected measurement result for each
participant (𝑄𝑖′ ), by using the drift of the standard ( 𝛿𝑄𝑑𝑟𝑓 ) to the mean measurement date of
TÜBİTAK UME by using Equation (13);
𝑄𝑖′ = 𝑄𝑖 − 𝛿𝑄𝑑𝑟𝑓
(13)
where,
𝛿𝑄𝑑𝑟𝑓 = 𝑚 × (𝑡𝑖 − 𝑡0 )
𝑚
(10-6 /day )
The drift of the travelling standard per day
𝑡𝑖
( days )
The average measurement date of the 𝑖 𝑡ℎ participant
𝑡0
( days )
The mean date of TÜBİTAK UME’s drift measurements (30.04.2019)
(14)
The standard uncertainties for corrected values of each participant are calculated by the following
equation:
𝑢(𝑄𝑖′ ) = √𝑢2 (𝑄𝑖 ) + 𝑢2 (𝛿𝑄𝑑𝑟𝑓 )
𝑢(𝑄𝑖′ )
The standard uncertainty of the corrected measurements of the participant (𝑄𝑖′ )
𝑢(𝑄𝑖 )
The standard uncertainty of the measurements of the participant (𝑄𝑖 )
(15)
𝑢(𝛿𝑄𝑑𝑟𝑓 ) The standard uncertainty of the correction values (𝛿𝑄𝑑𝑟𝑓 )
The errors reported by the participants (𝑄𝑖 ), the correction values (𝛿𝑄𝑑𝑟𝑓 ), the corrected results (𝑄𝑖′ )
and their corresponding expanded uncertainties (𝑈(𝑄𝑖 ), 𝑈(𝛿𝑄𝑑𝑟𝑓 ) and 𝑈(𝑄𝑖′ )) are presented in
Table 6 to Table 20.
The expanded uncertainty for the corrected values for was calculated by using
𝑈(𝑄𝑖′ ) = 𝑘 ∙ 𝑢(𝑄𝑖′ )
(16)
where, k is the coverage factor corresponding 95.45 % level of confidence.
28
The uncertainty of the correction values (𝛿𝑄𝑑𝑟𝑓 ) was calculated using the following equation.
𝑢(𝛿𝑄𝑑𝑟𝑓 ) = √𝑢(𝑄0 )2 + 𝑡 2 ∙ 𝑢(𝑚)2 + 2 ∙ 𝑡 ∙ 𝑐𝑜𝑣(𝑄0 , 𝑚)
(17)
Then, the comparison reference value is calculated by corrected results of the participants:
𝑄𝑖′
𝑢(𝑄𝑖′ )2
1
∑𝑟𝑖=1
𝑄𝑟𝑒𝑓 =
∑r𝑖=1
(18)
2
𝑢(𝑄𝑖′ )
The uncertainty of the comparison reference value, which is calculated by using the corrected
results, is calculated by:
𝑟
1
1
=∑ 2 ′
2
𝑢 (𝑄𝑟𝑒𝑓 )
𝑢 (𝑄𝑖 )
(19)
𝑖=1
The expanded uncertainty of the Comparison Reference Values (𝑄𝑟𝑒𝑓 ) was calculated by:
𝑈(𝑄𝑟𝑒𝑓 ) = 2 × 𝑢(𝑄𝑟𝑒𝑓 )
(20)
The results presented in Section 10.2 show that the chi-squared distributions (𝐹𝑁 (𝑄𝑖′ ) & 𝐹𝑟 (𝑄𝑖′ )),
observed Chi-square values (𝝌𝟐(N – 1; 0.05) & 𝝌𝟐(r – 1; 0.05) ), the result of the consistency test, if the
consistency test was failed, the outlier(s) which its result was excluded from the Comparison
Reference Value and the Comparison Reference Values (𝑄𝑟𝑒𝑓 ) and corresponding uncertainties
(𝑈(𝑄𝑟𝑒𝑓 )).
The results of the comparison are reported as the degrees of equivalence and the normalised error
between a participant’s result and the Comparison Reference Values (𝑄𝑟𝑒𝑓 ).
The degree of equivalence of each participant (𝑑𝑖 ), was calculated as:
𝑑𝑖 = 𝑄𝑖′ − 𝑄𝑟𝑒𝑓
(21)
where 𝑄𝑖′ is the corrected result of the participants due to the drift of the travelling standard with time,
and 𝑄𝑟𝑒𝑓 is the Comparison Reference Value.
29
The standard uncertainty of the degree of equivalence for a participant’s result (𝑈(𝑑𝑖 )), was
calculated as:
2
2
2
2
𝑢(𝑑𝑖 ) = √𝑢(𝑄′𝑖 ) + 𝑢 (𝑄𝑟𝑒𝑓 )
𝑢(𝑑𝑖 ) = √𝑢(𝑄𝑖′ ) − 𝑢(𝑄𝑟𝑒𝑓 )
for the discarded results
(22)
for the undiscarded results
(23)
where 𝑢(𝑄𝑖′ ) is the standart uncertainty of the corrected results of each participant and 𝑢(𝑄𝑟𝑒𝑓 ) is the
standard uncertainty of the Comparison Reference Value. Equation (22) was used where the
participant result does not contribute to the Comparison Reference Value. The expanded uncertainty
of the degree of equivalence is obtained by using the expansion factor k=2. Due to the correlation
with the Comparison Reference Value, Equation (23) was used where the participant result
contributes to the Comparison Reference Value.
The degree of equivalences and the normalised errors for each measurement point are presented in
Section 10.2.
10.1.3. Modification due to further instabilities of the transfer standard
During the evaluation of Q(-) values of 0.95 pA measurement results, we had to discard 5 of 7
participants to pass the consistency test. Since we thought that this situation is unconceivable, we
prefer to use the method used in EURAMET.EM-S24. According to the approach used in
EURAMET.EM-S24, even if the linear drift is subtracted, there is a remaining superimposed
instability, as can be seen for example in Figure 17.
Q(corr)
0.95 pA
Q(+)
Q(-)
1,002000
1,001800
1,001600
1,001400
1,001200
1,001000
1,000800
1,000600
1,000400
Figure 17. 0.95 pA measurement results of pilot laboratory
(Q(corr): The effect of the drift due to the time was eliminated)
30
For a proper description of the transfer instruments, this instability has to be taken into account. This
judgement is supported by initial calculations which show that, if this instability is not taken into
account in Q(-) values of 0.95 pA, the largest consistent data set consists of only 2 participants from
7 participants. But the largest consistent data set consist of 4 participants if this instability is taken
into account. We did not see such effect in 95 pA and 9.5 pA values.
Q
95 fA
Q(+)
Q(-)
1,00800
1,00600
1,00400
1,00200
1,00000
0,99800
0,99600
0,99400
Figure 18. 95 fA measurement results of pilot laboratory
Q
9.5 fA
Q(+)
Q(-)
1,08000
1,06000
1,04000
1,02000
1,00000
0,98000
0,96000
0,94000
0,92000
Figure 19. 9.5 fA measurement results of pilot laboratory
31
However, in addition to 0.95 pA measurements, the instability of the transfer instrument is significant
for 95 fA and 9.5 fA measurements in comparison to the uncertainty values of some participants.
Thus, we decided to take into account the instability values of the transfer instrument for 95 fA and
9.5 fA as well as 0.95 pA measurements. The merged graphical representations of Q(+) and Q(-)
values for 95 fA and 9.5 fA measurement results of the pilot laboratory are shown in Figure 18 and
Figure 19.
In order to describe this type of instabilitiy of the transfer standard, an additional uncertainty term
u(ts) is defined. After the drift effect are corrected in the measurement results of the pilot laboratory
(which were only used to determine drift values of the transfer instrument), the results in Figure 17
were obtained. 95 fA and 9.5 fA measurements of the pilot laboratory can be seen in Figure 18 and
Figure 19.
The uncertainty term u(ts) is determined by using the standard deviations σ(Q+) for the positive
current direction and σ(Q-) for the negative current direction of the measurement results of the pilot
laboratory that can be seen in Figure 17, 18 and 19.
As a result, for 0.95 pA measurements, a drift has to be taken into account and with the
corresponding standard deviations after correction of linear time drift. However, we could not detect
a linear drift in 95 fA and 9.5 fA measurements, which is explained in Section 9.2. We assume that
the instability is due to the transfer standard as well as the pilot laboratory’s calibration set-up.
As u(ts) depends on the same internal components of the transfer instruments, it should be the
same for both current directions. It is estimated as:
𝑢(𝑡𝑠) =
𝜎(𝑄+ ) + 𝜎(𝑄− )
2
(24)
Taking into account u(ts), Equation 5 will be as follows:
𝑒𝑖 (𝑄𝑟𝑒𝑓 ) =
(𝑄𝑖 − 𝑄𝑟𝑒𝑓 )2
𝑢2 (𝑄𝑖′ ) + 𝑢2 (𝑡𝑠)
(25)
The comparison reference value is calculated by:
∑𝑟𝑖=1
𝑄𝑟𝑒𝑓 =
∑r𝑖=1
𝑢(𝑄𝑖′ )2
𝑄𝑖′
+ 𝑢2 (𝑡𝑠)
1
2
𝑢(𝑄𝑖′ )
+ 𝑢2 (𝑡𝑠)
(26)
32
The uncertainty of the comparison reference value is calculated by the following equation:
𝑟
1
1
=∑ 2 ′
2
𝑢 (𝑄𝑟𝑒𝑓 )
𝑢 (𝑄𝑖 ) + 𝑢2 (𝑡𝑠)
(27)
𝑖=1
For each result 𝑄𝑖′ , a function ei (Qref) is defined in Equation 25 by using the last 𝑢(𝑄𝑖′ ) values. The
determination of the largest consistent subset of the participant results was obtained as explained in
section 10.1.1.
The standard uncertainty of the degree of equivalence for a participant’s result (𝑢(𝑑𝑖 )), was
calculated as:
2
2
2
2
𝑢(𝑑𝑖 ) = √𝑢(𝑄′𝑖 ) + 𝑢 (𝑄𝑟𝑒𝑓 ) + 𝑢2 (𝑡𝑠)
𝑢(𝑑𝑖 ) = √𝑢(𝑄𝑖′ ) − 𝑢(𝑄𝑟𝑒𝑓 ) + 𝑢2 (𝑡𝑠)
for the discarded results
(28)
for the undiscarded results
(29)
Equation 28 was used where the participant result does not contribute to the Comparison Reference
Value. The expanded uncertainty of the degree of equivalence 𝑈(𝑑𝑖 ) is obtained by using the
expansion factor k=2. Due to the correlation with the Comparison Reference Value, Equation 29 was
used where the participant result contributes to the Comparison Reference Value.
33
10.2. Measurement Results
Mean Date of the measurements of TÜBİTAK UME for monitoring the drift: 30.04.2019
𝑸𝒊
Measurement result of each participant
𝑼(𝑸𝒊 )
Expanded measurement uncertainty of measurement result of each participant
𝜹𝑸𝒅𝒓𝒇
The drift of the standard to the mean date of TÜBİTAK UME’s drift measurements
𝑼(𝜹𝑸𝒅𝒓𝒇 ) Expanded uncertainty for the drift of the standard
𝒆𝒊
Indication if the result had to be discarded from calculating the reference value due to a too large value of 𝑒𝑖
𝑸′𝒊
The corrected measurement result of each participant to the mean date
𝑼(𝑸′𝒊 )
𝒅𝒊
Expanded measurement uncertainty of the corrected measurement result of each participant
Degree of equivalence
𝑼(𝒅𝒊 )
The expanded uncertainty of the degree of equivalence for each participant’s result
u(ts)
The standard deviation of the measurements performed by TUBITAK UME to monitor the stability of the transfer standard
(after the effect of the drift due to the time was eliminated)
34
Table 6. Results for 95 pA, positive current direction
Reference value: Qref = 1.000482, U(Qref) = 0.000041
Institute
Measurement
Date
𝑸𝒊
𝑼(𝑸𝒊 )
𝜹𝑸𝒅𝒓𝒇
𝒖(𝜹𝑸𝒅𝒓𝒇 )
(v = 8)
𝑸′𝒊
𝑼(𝑸′𝒊 )
𝒆𝒊
Discard
𝒅𝒊
𝑼(𝒅𝒊 )
TÜBİTAK UME
14.03.2018
1.000274
0.000050
-0.000042
0.000005
1.000316
0.000051
42.05
Y
-0.000166
0.000059
LNE
03.05.2018
1.000410
0.000095
-0.000037
0.000005
1.000447
0.000096
0.52
N
-0.000035
0.000091
NSAI
12.06.2018
1.000440
0.000280
-0.000033
0.000005
1.000473
0.000280
0.00
N
-0.000009
0.000278
METAS
18.09.2018
1.000445
0.000043
-0.000023
0.000005
1.000468
0.000044
0.38
N
-0.000014
0.000032
HU-BFKH
18.10.2018
1.000490
0.000066
-0.000020
0.000005
1.000510
0.000067
0.72
N
0.000028
0.000059
RISE
21.11.2018
1.000487
0.000069
-0.000016
0.000005
1.000503
0.000070
0.39
N
0.000021
0.000063
IPQ
03.06.2019
1.000795
0.002399
0.000004
0.000005
1.00079
0.00240
0.07
N
0.00031
0.00240
35
1,004000
Q
+95 pA Q(+)
1,003000
1,002000
1,001000
1,000000
0,999000
0,998000
UME
LNE
NSAI
METAS
HU-BFKH
RISE
IPQ
Figure 18. Calibration factors for the Keithley at 95 pA for positive current direction, together with
the reference line (solid line) and its uncertainty for k=2 (dashed lines).
1,000900
Q
+95 pA Q(+)
1,000800
1,000700
1,000600
1,000500
1,000400
1,000300
1,000200
1,000100
UME
LNE
NSAI
METAS
HU-BFKH
RISE
IPQ
Figure 19. Calibration factors in zoomed scale for the Keithley at 95 pA for positive current direction,
together with the reference line (solid line) and its uncertainty for k=2 (dashed lines). Results not
shown in the graph are located outside of the plotting.
36
Table 7. Results for 95 pA, negative current direction
Reference value: Qref = 1.000433, U(Qref) = 0.000042
Measurement
Date
𝑸𝒊
𝑼(𝑸𝒊 )
𝜹𝑸𝒅𝒓𝒇
𝒖(𝜹𝑸𝒅𝒓𝒇 )
(v = 8)
𝑸′𝒊
𝑼(𝑸′𝒊 )
𝒆𝒊
Discard
𝒅𝒊
𝑼(𝒅𝒊 )
TÜBİTAK UME
14.03.2018
1.000242
0.000050
-0.000040
0.000006
1.000282
0.000051
34.13
Y
-0.000151
0.000060
LNE
3.05.2018
1.000360
0.000096
-0.000035
0.000006
1.000395
0.000096
0.59
N
-0.000038
0.000091
NSAI
12.06.2018
1.000400
0.000280
-0.000032
0.000006
1.000432
0.000280
0,00
N
-0.000001
0.000278
METAS
18.09.2018
1.000369
0.000045
-0.000022
0.000006
1.000391
0.000047
3.24
N
-0.000042
0.000034
HU-BFKH
18.10.2018
1.000482
0.000066
-0.000019
0.000006
1.000501
0.000067
4.17
N
0.000068
0.000059
RISE
21.11.2018
1.000457
0.000069
-0.000016
0.000006
1.000473
0.000070
1.32
N
0.000040
0.000062
IPQ
5.06.2019
1.000201
0.001432
0.000004
0.000006
1.00020
0.00143
0.11
N
-0.00023
0.00143
Institute
37
1,002000
Q
-95 pA Q(-)
1,001500
1,001000
1,000500
1,000000
0,999500
0,999000
0,998500
0,998000
UME
LNE
NSAI
METAS
HU-BFKH
RISE
IPQ
Figure 20. Calibration factors for the Keithley at 95 pA for negative current direction, together with
the reference line (solid line) and its uncertainty for k=2 (dashed lines).
1,000800
Q
-95 pA Q(-)
1,000700
1,000600
1,000500
1,000400
1,000300
1,000200
1,000100
UME
LNE
NSAI
METAS
HU-BFKH
RISE
IPQ
Figure 21. Calibration factors in zoomed scale for the Keithley at 95 pA for negative current
direction, together with the reference line (solid line) and its uncertainty for k=2 (dashed lines).
Results not shown in the graph are located outside of the plotting.
38
Table 8. Results for 95 pA, mean of both current directions
Reference value: Qref = 1.000457, U(Qref) = 0.000041
Institute
Measurement
Date
𝑸′𝒊
𝑼(𝑸′𝒊 )
𝒆𝒊
Discard
𝒅𝒊
𝑼(𝒅𝒊 )
TÜBİTAK UME
14.03.2018
1.000299
0.000051
37.84
Y
-0.000158
0.000060
LNE
3.05.2018
1.000421
0.000096
0.55
N
-0.000036
0.000091
NSAI
12.06.2018
1.000452
0.000280
0.00
N
-0.000005
0.000278
METAS
18.09.2018
1.000429
0.000045
1.47
N
-0.000028
0.000033
HU-BFKH
18.10.2018
1.000505
0.000067
2.11
N
0.000048
0.000059
RISE
21.11.2018
1.000488
0.000070
0.80
N
0.000031
0.000062
IPQ
4.06.2019
1.00049
0.00192
0.00
N
0.00003
0.00192
39
1,003000
Q
95 pA Q(mean)
1,002500
1,002000
1,001500
1,001000
1,000500
1,000000
0,999500
0,999000
0,998500
0,998000
UME
LNE
NSAI
METAS
HU-BFKH
RISE
IPQ
Figure 22. Calibration factors for the Keithley at 95 pA for mean of both current directions, together
with the reference line (solid line) and its uncertainty for k=2 (dashed lines).
1,000800
Q
95 pA Q(mean)
1,000700
1,000600
1,000500
1,000400
1,000300
1,000200
1,000100
UME
LNE
NSAI
METAS
HU-BFKH
RISE
IPQ
Figure 23. Calibration factors in zoomed scale for the Keithley at 95 pA for mean of both current
directions, together with the reference line (solid line) and its uncertainty for k=2 (dashed lines).
Results not shown in the graph are located outside of the plotting.
40
Table 9. Results for 9.5 pA, positive current direction
Reference value: Qref = 1.001397, U(Qref) = 0.000070
Institute
Measurement
Date
𝑸𝒊
𝑼(𝑸𝒊 )
𝜹𝑸𝒅𝒓𝒇
𝒖(𝜹𝑸𝒅𝒓𝒇 )
(v = 7)
𝑸′𝒊
𝑼(𝑸′𝒊 )
𝒆𝒊
Discard
𝒅𝒊
𝑼(𝒅𝒊 )
TÜBİTAK UME
14.03.2018
1.000981
0.000120
-0.000125
0.000015
1.001106
0.000124
22.12
Y
-0.000291
0.000133
LNE
1.05.2018
1.001430
0.000214
-0.000110
0.000015
1.001540
0.000216
1.76
N
0.000143
0.000211
NSAI
11.06.2018
1.001460
0.000320
-0.000098
0.000015
1.001558
0.000321
1.00
N
0.000161
0.000318
METAS
18.09.2018
1.001333
0.000056
-0.000068
0.000015
1.001400
0.000064
0.01
N
0.000003
0.000041
HU-BFKH
21.10.2018
1.000679
0.000146
-0.000058
0.000015
1.000737
0.000149
78.39
Y
-0.000660
0.000157
RISE
20.11.2018
1.001313
0.000077
-0.000049
0.000015
1.001362
0.000082
0.73
N
-0.000035
0.000067
IPQ
9.06.2019
1.000885
0.001623
0.000012
0.000015
1.00087
0.00162
0.42
N
-0.00053
0.00162
41
1,003000
Q
+9.5 pA Q(+)
1,002500
1,002000
1,001500
1,001000
1,000500
1,000000
0,999500
0,999000
0,998500
0,998000
UME
LNE
NSAI
METAS
HU-BFKH
RISE
IPQ
Figure 24. Calibration factors for the Keithley at 9.5 pA for positive current direction, together with
the reference line (solid line) and its uncertainty for k=2 (dashed lines).
Q
+9.5 pA Q(+)
1,001900
1,001700
1,001500
1,001300
1,001100
1,000900
1,000700
1,000500
UME
LNE
NSAI
METAS
HU-BFKH
RISE
IPQ
Figure 25. Calibration factors in zoomed scale for the Keithley at 9.5 pA for positive current
direction, together with the reference line (solid line) and its uncertainty for k=2 (dashed lines).
Results not shown in the graph are located outside of the plotting.
42
Table 10. Results for 9.5 pA, negative current direction
Reference value: Qref = 1.001248, U(Qref) = 0.000055
Institute
Measurement
Date
𝑸𝒊
𝑼(𝑸𝒊 )
𝜹𝑸𝒅𝒓𝒇
𝒖(𝜹𝑸𝒅𝒓𝒇 )
(v = 6)
𝑸′𝒊
𝑼(𝑸′𝒊 )
𝒆𝒊
Discard
𝒅𝒊
𝑼(𝒅𝒊 )
TÜBİTAK UME
14.03.2018
1.000872
0.000120
-0.000083
0.000008
1.000955
0.000121
23.42
Y
-0.000293
0.000129
LNE
1.05.2018
1.001300
0.000216
-0.000074
0.000008
1.001374
0.000217
1.34
N
0.000126
0.000212
NSAI
11.06.2018
1.001380
0.000320
-0.000065
0.000008
1.001445
0.000320
1.51
N
0.000197
0.000317
METAS
18.09.2018
1.001180
0.000056
-0.000045
0.000008
1.001226
0.000058
0.61
N
-0.000022
0.000039
HU-BFKH
21.10.2018
1.001117
0.000146
-0.000039
0.000008
1.001156
0.000147
1.60
N
-0.000092
0.000140
RISE
20.11.2018
1.001259
0.000077
-0.000033
0.000008
1.001292
0.000078
1.22
N
0.000044
0.000065
IPQ
5.06.2019
0.999997
0.001407
0.000007
0.000008
0.99999
0.00141
3.20
N
-0.00126
0.00141
43
1,002000
Q
-9.5 pA Q(-)
1,001500
1,001000
1,000500
1,000000
0,999500
0,999000
0,998500
0,998000
UME
LNE
NSAI
METAS
HU-BFKH
RISE
IPQ
Figure 26. Calibration factors for the Keithley at 9.5 pA for negative current direction, together with
the reference line (solid line) and its uncertainty for k=2 (dashed lines).
1,001700
Q
-9.5 pA Q(-)
1,001600
1,001500
1,001400
1,001300
1,001200
1,001100
1,001000
1,000900
1,000800
UME
LNE
NSAI
METAS
HU-BFKH
RISE
IPQ
Figure 27. Calibration factors in zoomed scale for the Keithley at 9.5 pA for negative current
direction, together with the reference line (solid line) and its uncertainty for k=2 (dashed lines).
Results not shown in the graph are located outside of the plotting.
44
Table 11. Results for 9.5 pA, mean of both current directions
Reference value: Qref = 1.001328, U(Qref) = 0.000067
Institute
Measurement
Date
𝑸′𝒊
𝑼(𝑸′𝒊 )
𝒆𝒊
Discard
𝒅𝒊
𝑼(𝒅𝒊 )
TÜBİTAK UME
14.03.2018
1.001031
0.000122
23.51
Y
-0.000297
0.000131
LNE
1.05.2018
1.001457
0.000216
1.43
N
0.000129
0.000211
NSAI
11.06.2018
1.001502
0.000321
1.18
N
0.000174
0.000317
METAS
18.09.2018
1.001313
0.000061
0.23
N
-0.000015
0.000039
HU-BFKH
21.10.2018
1.000946
0.000148
26.56
Y
-0.000382
0.000155
RISE
20.11.2018
1.001327
0.000080
0.00
N
-0.000001
0.000065
IPQ
7.06.2019
1.00043
0.00152
1.40
N
-0.00090
0.00151
45
1,002500
Q
9.5 pA Q(mean)
1,002000
1,001500
1,001000
1,000500
1,000000
0,999500
0,999000
0,998500
0,998000
UME
LNE
NSAI
METAS
HU-BFKH
RISE
IPQ
Figure 28. Calibration factors for the Keithley at 9.5 pA for mean of both current directions, together
with the reference line (solid line) and its uncertainty for k=2 (dashed lines).
1,001900
Q
9.5 pA Q(mean)
1,001700
1,001500
1,001300
1,001100
1,000900
1,000700
UME
LNE
NSAI
METAS
HU-BFKH
RISE
IPQ
Figure 29. Calibration factors in zoomed scale for the Keithley at 9.5 pA for mean of both current
directions, together with the reference line (solid line) and its uncertainty for k=2 (dashed lines).
Results not shown in the graph are located outside of the plotting.
46
Table 12. Results for 0.95 pA, positive current direction*
Reference value: Qref = 1.002558, U(Qref) = 0.000499, u(ts) = 0.000094
Institute
Measurement
Date
𝑸𝒊
𝑼(𝑸𝒊 )
𝜹𝑸𝒅𝒓𝒇
𝒖(𝜹𝑸𝒅𝒓𝒇 )
(v = 7)
𝑸′𝒊
𝑼(𝑸′𝒊 )
𝒆𝒊
Discard
𝒅𝒊
𝑼(𝒅𝒊 )
TÜBİTAK UME
14.03.2018
1.000974
0.000500
-0.000215
0.000046
1.001189
0.000508
25.49
Y
-0.001369
0.000585
LNE
26.04.2018
1.002900
0.000888
-0.000193
0.000046
1.003093
0.000893
1.38
N
0.000535
0.000885
NSAI
11.06.2018
1.002670
0.000574
-0.000169
0.000046
1.002839
0.000581
0.85
N
0.000281
0.000570
METAS
18.09.2018
1.002357
0.000122
-0.000117
0.000046
1.002474
0.000156
0.47
N
-0.000084
0.000106
HU-BFKH
21.10.2018
0.999299
0.001162
-0.000100
0.000046
0.99940
0.00117
28.64
Y
-0.00316
0.00120
RISE
19.11.2018
1.002030
0.000070
-0.000085
0.000046
1.002115
0.000125
15.38
Y
-0.000443
0.000316
* : IPQ did not perform (+)0.95 pA measurements.
47
Q
+0.95 pA Q(+)
1,0070
1,0050
1,0030
1,0010
0,9990
0,9970
0,9950
UME
LNE
NSAI
METAS
HU-BFKH
RISE
Figure 30. Calibration factors for the Keithley at 0.95 pA for positive current direction, together with
the reference line (solid line) and its uncertainty for k=2 (dashed lines).
Q
+0.95 pA Q(+)
1,0040
1,0035
1,0030
1,0025
1,0020
1,0015
1,0010
UME
LNE
NSAI
METAS
HU-BFKH
RISE
Figure 31. Calibration factors in zoomed scale for the Keithley at 0.95 pA for positive current
direction, together with the reference line (solid line) and its uncertainty for k=2 (dashed lines).
Results not shown in the graph are located outside of the plotting.
48
Table 13. Results for 0.95 pA, negative current direction
Reference value: Qref = 1.002197, U(Qref) = 0.000254, u(ts) = 0.000094
Institute
Measurement
Date
𝑸𝒊
𝑼(𝑸𝒊 )
𝜹𝑸𝒅𝒓𝒇
𝒖(𝜹𝑸𝒅𝒓𝒇 )
(v = 7)
𝑸′𝒊
𝑼(𝑸′𝒊 )
𝒆𝒊
Discard
𝒅𝒊
𝑼(𝒅𝒊 )
TÜBİTAK UME
14.03.2018
1.000972
0.000500
-0.000227
0.000036
1.001199
0.000505
13.69
Y
-0,000998
0,000561
LNE
26.04.2018
1.002800
0.000850
-0.000204
0.000036
1.003004
0.000853
3.41
Y
0,000807
0,000887
NSAI
11.06.2018
1.002570
0.000574
-0.000178
0.000036
1.002748
0.000578
3.29
N
0,000551
0,000589
METAS
18.09.2018
1.002154
0.000122
-0.000124
0.000036
1.002278
0.000141
0.48
N
0,000081
0,000178
HU-BFKH
21.10.2018
1.004027
0.001162
-0.000105
0.000036
1.00413
0.00116
10.77
Y
0,00193
0,00119
RISE
19.11.2018
1.001978
0.000070
-0.000089
0.000036
1.002067
0.000106
1.43
N
-0,000130
0,000152
IPQ
14.06.2019
1.000027
0.003431
0.000025
0.000036
1.00000
0.00343
1.63
N
-0,00220
0,00343
49
Q
-0.95 pA Q(-)
1,0060
1,0040
1,0020
1,0000
0,9980
0,9960
UME
LNE
NSAI
METAS
HU-BFKH
RISE
IPQ
Figure 32. Calibration factors for the Keithley at 0.95 pA for negative current direction, together with
the reference line (solid line) and its uncertainty for k=2 (dashed lines).
Q
-0.95 pA Q(-)
1,0040
1,0035
1,0030
1,0025
1,0020
1,0015
1,0010
1,0005
UME
LNE
NSAI
METAS
HU-BFKH
RISE
IPQ
Figure 33. Calibration factors in zoomed scale for the Keithley at 0.95 pA for negative current
direction, together with the reference line (solid line) and its uncertainty for k=2 (dashed lines).
Results not shown in the graph are located outside of the plotting.
50
Table 14. Results for 0.95 pA, mean of both current directions*
Reference value: Qref = 1.002252, U(Qref) = 0.000257, u(ts) = 0.000094
Institute
Measurement
Date
𝑸′𝒊
𝑼(𝑸′𝒊 )
𝒆𝒊
Discard
𝒅𝒊
𝑼(𝒅𝒊 )
TÜBİTAK UME
14.03.2018
1.001195
0.000507
15.29
Y
-0.001057
0.000563
LNE
26.04.2018
1.003048
0.000873
3.18
Y
0.000796
0.000906
NSAI
11.06.2018
1.002794
0.000580
3.16
N
0.000542
0.000590
METAS
18.09.2018
1.002376
0.000149
1.07
N
0.000124
0.000183
HU-BFKH
21.10.2018
1.00177
0.00116
0.68
N
-0.00048
0.00117
RISE
19.11.2018
1.002091
0.000115
2.12
N
-0.000161
0.000157
* : IPQ did not perform (+)0.95 pA measurements. Thus, there is no “mean” value for IPQ.
1,0040
Q
0.95 pA Q(mean)
1,0035
1,0030
1,0025
1,0020
1,0015
1,0010
1,0005
UME
LNE
NSAI
METAS
HU-BFKH
RISE
Figure 34. Calibration factors for the Keithley at 0.95 pA for mean of both current directions,
together with the reference line (solid line) and its uncertainty for k=2 (dashed lines).
51
Table 15. Results for 95 fA, positive current direction*
Reference value: Qref = 1.002575, U(Qref) = 0.001044
Institute
Measurement
Date
𝑸𝒊
𝑼(𝑸𝒊 )
𝒆𝒊
Discard
𝒅𝒊
𝑼(𝒅𝒊 )
TÜBİTAK UME
14.03.2018
1.00090
0.00360
0.83
N
-0.00167
0.00359
LNE
22.04.2018
1.00380
0.00916
0.07
N
0.00123
0.00916
NSAI
12.06.2018
1.00270
0.00420
0.00
N
0.00013
0.00419
METAS
18.09.2018
1.00239
0.00116
0.07
N
-0.00018
0.00114
RISE
15.11.2018
1.00279
0.00069
0.18
N
0.00022
0.00066
IPQ
12.06.2019
0.9981
0.0332
0.07
N
-0.0045
0.0332
* : HU-BFKH did not perform (+)95 fA measurements.
52
1,040000
Q
+95 fA Q(+)
1,030000
1,020000
1,010000
1,000000
0,990000
0,980000
0,970000
0,960000
UME
LNE
NSAI
METAS
RISE
IPQ
Figure 35. Calibration factors for the Keithley at 95 fA for positive current direction, together with the
reference line (solid line) and its uncertainty for k=2 (dashed lines).
Q
+95 fA Q(+)
1,013000
1,008000
1,003000
0,998000
0,993000
UME
LNE
NSAI
METAS
RISE
IPQ
Figure 36. Calibration factors in zoomed scale for the Keithley at 95 fA for positive current direction,
together with the reference line (solid line) and its uncertainty for k=2 (dashed lines). Results not
shown in the graph are located outside of the plotting.
53
Table 16. Results for 95 fA, negative current direction
Reference value: Qref = 1.000669, U(Qref) = 0.000993
Measurement
Date
𝑸𝒊
𝑼(𝑸𝒊 )
𝒆𝒊
Discard
𝒅𝒊
𝑼(𝒅𝒊 )
TÜBİTAK UME
14.03.2018
1.00040
0.00360
0.02
N
-0.00027
0.00359
LNE
22.04.2018
1.00240
0.00940
0.13
N
0.00173
0.00940
NSAI
12.06.2018
1.00270
0.00420
0.91
N
0.00203
0.00419
METAS
18.09.2018
1.00223
0.00118
4.96
N
0.00156
0.00116
HU-BFKH
6.11.2018
1.0003
0.0116
0.00
N
-0.0004
0.0116
RISE
15.11.2018
0.99967
0.00069
3.79
N
-0.00100
0.00066
IPQ
13.06.2019
1.0150
0.0175
2.70
N
0.0143
0.0175
Institute
54
1,0350
Q
-95 fA Q(-)
1,0300
1,0250
1,0200
1,0150
1,0100
1,0050
1,0000
0,9950
0,9900
0,9850
UME
LNE
NSAI
METAS
HU-BFKH
RISE
IPQ
Figure 37. Calibration factors for the Keithley at 95 fA for negative current direction, together with
the reference line (solid line) and its uncertainty for k=2 (dashed lines).
Q
-95 fA Q(-)
1,0130
1,0080
1,0030
0,9980
0,9930
0,9880
UME
LNE
NSAI
METAS
HU-BFKH
RISE
IPQ
Figure 38. Calibration factors in zoomed scale for the Keithley at 95 fA for negative current
direction, together with the reference line (solid line) and its uncertainty for k=2 (dashed lines).
Results not shown in the graph are located outside of the plotting.
55
Table 17. Results for 95 fA, mean of both current directions*
Reference value: Qref = 1.001618, U(Qref) = 0.001046
Institute
Measurement
Date
𝑸′𝒊
𝑼(𝑸′𝒊 )
𝒆𝒊
Discard
𝒅𝒊
𝑼(𝒅𝒊 )
TÜBİTAK UME
14.03.2018
1.00065
0.00360
0.28
N
-0.00097
0.00359
LNE
22.04.2018
1.00310
0.00928
0.10
N
0.00148
0.00928
NSAI
12.06.2018
1.00270
0.00420
0.26
N
0.00108
0.00419
METAS
18.09.2018
1.00231
0.00117
0.98
N
0.00069
0.00115
RISE
15.11.2018
1.00123
0.00069
0.57
N
-0.00039
0.00066
IPQ
13.06.2019
1.0066
0.0253
0.15
N
0.0050
0.0253
* : HU-BFKH did not perform (+)95 fA measurements. Thus, there is no “mean” value for HU-BFKH.
56
1,0400
Q
95 fA Q(mean)
1,0300
1,0200
1,0100
1,0000
0,9900
0,9800
0,9700
UME
LNE
NSAI
METAS
RISE
IPQ
Figure 39. Calibration factors for the Keithley at 95 fA for mean of both current directions, together
with the reference line (solid line) and its uncertainty for k=2 (dashed lines).
1,0150
Q
95 fA Q(mean)
1,0100
1,0050
1,0000
0,9950
0,9900
UME
LNE
NSAI
METAS
RISE
IPQ
Figure 40. Calibration factors in zoomed scale for the Keithley at 95 fA for mean of both current
directions, together with the reference line (solid line) and its uncertainty for k=2 (dashed lines).
Results not shown in the graph are located outside of the plotting.
57
Table 18. Results for 9.5 fA, positive current direction*000000000
Reference value: Qref = 1.00155, U(Qref) = 0.01059
Measurement
Date
𝑸𝒊
𝑼(𝑸𝒊 )
𝒆𝒊
TÜBİTAK UME
14.03.2018
1.0049
0.0360
0.03
LNE
18.04.2018
1.0088
0.0748
NSAI
15.06.2018
1.0023
METAS
20.09.2018
RISE
IPQ
Institute
𝒅𝒊
𝑼(𝒅𝒊 )
N
0.0033
0.0365
0.04
N
0.0072
0.0750
0.0340
0.00
N
0.0008
0.0345
1.00274
0.00516
0.04
N
0.00119
0.00797
16.11.2018
0.99940
0.00798
0.11
N
-0.0021
0.0100
14.06.2019
0.967
0.265
0.07
N
-0.035
0.265
Discard
* : HU-BFKH did not perform (+)9.5 fA measurements.
58
Q
+9.5 fA Q(+)
1,3500
1,2500
1,1500
1,0500
0,9500
0,8500
0,7500
0,6500
UME
LNE
NSAI
METAS
RISE
IPQ
Figure 41. Calibration factors for the Keithley at 9.5 fA for positive current direction, together with
the reference line (solid line) and its uncertainty for k=2 (dashed lines).
1,0900
Q
+9.5 fA Q(+)
1,0700
1,0500
1,0300
1,0100
0,9900
0,9700
0,9500
0,9300
UME
LNE
NSAI
METAS
RISE
IPQ
Figure 42. Calibration factors in zoomed scale for the Keithley at 9.5 fA for positive current direction,
together with the reference line (solid line) and its uncertainty for k=2 (dashed lines). Results not
shown in the graph are located outside of the plotting.
59
Table 19. Results for 9.5 fA, negative current direction
Reference value: Qref = 1.00134, U(Qref) = 0.01018
Institute
Measurement
Date
𝑸𝒊
𝑼(𝑸𝒊 )
𝒆𝒊
Discard
𝒅𝒊
𝑼(𝒅𝒊 )
TÜBİTAK UME
14.03.2018
0.9957
0.0360
0.09
N
-0.0056
0.0365
LNE
18.04.2018
1.0021
0.0696
0.00
N
0.0008
0.0699
NSAI
15.06.2018
1.0028
0.0340
0.01
N
0.0015
0.0345
METAS
20.09.2018
1.00250
0.00586
0.04
N
0.00116
0.00835
HU-BFKH
6.11.2018
0.937
0.116
1.22
N
-0.064
0.116
RISE
16.11.2018
1.00110
0.00798
0.00
N
-0.0002
0.0100
IPQ
13.06.2019
1.018
0.202
0.03
N
0.017
0.202
60
Q
-9.5 fA Q(-)
1,3500
1,2500
1,1500
1,0500
0,9500
0,8500
0,7500
0,6500
UME
LNE
NSAI
METAS
HU-BFKH
RISE
IPQ
Figure 43. Calibration factors for the Keithley at 9.5 fA for negative current direction, together with
the reference line (solid line) and its uncertainty for k=2 (dashed lines).
Q
-9.5 fA Q(-)
1,0800
1,0600
1,0400
1,0200
1,0000
0,9800
0,9600
0,9400
0,9200
UME
LNE
NSAI
METAS
HU-BFKH
RISE
IPQ
Figure 44. Calibration factors in zoomed scale for the Keithley at 9.5 fA for negative current
direction, together with the reference line (solid line) and its uncertainty for k=2 (dashed lines).
Results not shown in the graph are located outside of the plotting.
61
Table 20. Results for 9.5 fA, mean of both current directions*
Reference value: Qref = 1.00160, U(Qref) = 0.01066
Institute
Measurement
Date
𝑸𝒊
𝑼(𝑸𝒊 )
𝒆𝒊
Discard
𝒅𝒊
𝑼(𝒅𝒊 )
TÜBİTAK UME
14.03.2018
1.0003
0.0360
0.00
N
-0.0013
0.0365
LNE
18.04.2018
1.0055
0.0722
0.01
N
0.0039
0.0724
NSAI
15.06.2018
1.0026
0.0340
0.00
N
0.0010
0.0345
METAS
20.09.2018
1.00262
0.00551
0.03
N
0.00102
0.00814
RISE
11.11.2018
1.00025
0.00798
0.04
N
-0.0013
0.0100
IPQ
1.03.2019
0.993
0.233
0.01
N
-0.009
0.233
* : HU-BFKH did not perform (+)9.5 fA measurements. Thus, there is no “mean” value for HU-BFKH.
62
Q
9.5 fA Q(mean)
1,3500
1,2500
1,1500
1,0500
0,9500
0,8500
0,7500
0,6500
UME
LNE
NSAI
METAS
RISE
IPQ
Figure 45. Calibration factors for the Keithley at 9.5 fA for mean of both current directions, together
with the reference line (solid line) and its uncertainty for k=2 (dashed lines).
Q
9.5 fA Q(mean)
1,0800
1,0600
1,0400
1,0200
1,0000
0,9800
0,9600
0,9400
0,9200
UME
LNE
NSAI
METAS
RISE
IPQ
Figure 46. Calibration factors in zoomed scale for the Keithley at 9.5 fA for mean of both current
directions, together with the reference line (solid line) and its uncertainty for k=2 (dashed lines).
Results not shown in the graph are located outside of the plotting.
63
11. Withdrawals or Change of Results
There were no changes of the results.
Based on a strong recommendation by the EURAMET Board of Directors, VNIIFTRI (Russia) was
excluded from the comparison and their measurement results were not considered any further,
neither in the data analysis nor in the comparison report.
12. Summary and Conclusions
The EURAMET.EM-S44 comparison was performed with 7 participants.
The objective of this comparison is to provide technical evidence supporting their CMCs entries of
those participants who did not participate in the EURAMET.EM-S24, while other participants would
have an evidence for confirmation of their improvements in this field of measurement.
Besides, ±9.5 fA measurements measurements have been performed in addition to the
measurement points of EURAMET.EM-S24.
A commercial electrometer Keithley 6430 was used as travelling standard. A linear drift of the
travelling standard was observed at ±95 pA, ±9.5 pA and ±0.95 pA values.Therefore, the effect of
the linear drift was eliminated for the evalution of the measurement results.
The comparison reference value has been determined based on the weighted mean of participant
results that survived outlier detection. The discarded results have been showed in the tables in
“Measurement Results” section.
Because of the Covid-19 pandemic conditions, some delays in customs and in sending the
participants reports, the comparison has taken longer time period than expected.
64
13. References
[1] CCEM Guidelines for Planning, Organizing, Conducting and Reporting Key, Supplementary and
Pilot Comparisons, Version 2.1, June 2017
[2] JCGM 100, "Evaluation of measurement data – Guide to the expression of uncertainty in
measurement (GUM)", 2008.
[3] Cox M. G., “The evaluation of key comparison data”, 2002 Metrologia 39, 589-595.
[4] Cox M. G., “The evaluation of key comparison data: determining the largest consistent subset”,
2007 Metrologia 44, 187.
[5] H. E. van den Brom, P. de la Court, and G. Rietveld, Accurate subpicoampere current source
based on a differentiating capacitor with software-controlled nonlinearity compensation, IEEE
Trans. Instrum. Meas. 54, pp. 554-558, 2005.
[6] O.Monnoye et al., “Calibration of high value resistors and very low currents”, Revue Française
de Métrologie, 2007.
[7] N. Ruchaud et al., Proceedings of the 2006 Conference on Precision Electromagnetic
Measurements, 2006.
[8] Tobias Bergsten et al., “A precision current source using Δ–Σ modulation”, IEEE Trans. Instrum.
Meas. 60, pp. 2341-2346, 2011.
65
Appendix A: Results of the participants in chronological order
TÜBİTAK UME
U
Temp.
Nom.
Current
(Temp.)
Press.
)
( °C
Humid.
(Press.)
Date
( °C
U
(mbar)
)
(mbar)
U
(Humid.)
(%rh)
(%rh)
Supplied
Current
(A)
Transfer
instrument’s
measuring
range
Reading of
transfer
instrument
( pA )
(A)
Ratio
(Measurement
result)
Q
Standard
uncertainty
of
Degrees
measurement
of
(combined
freedom
type A and B)
U
k
(k·u(Q))
u(Q)
+9.5 fA
14.03.2018
23.0
0.5
1000
15
45
10
9.508·10-15
1
-9.555·10-15
1.0049
1.8 ∙ 10-2
>100
2
3.6 ∙ 10-2
-9.5 fA
14.03.2018
23.0
0.5
1000
15
45
10
-9.508·10-15
1
9.467·10-15
0.9957
1.8 ∙ 10-2
>100
2
3.6 ∙ 10-2
+95 fA
14.03.2018
23.0
0.5
1000
15
45
10
95.064·10-15
1
-95.150·10-15
1.000903
1.8 ∙ 10-3
>100
2
3.6 ∙ 10-3
-95 fA
14.03.2018
23.0
0.5
1000
15
45
10
-95.063·10-15
1
95.101·10-15
1.000399
1.8 ∙ 10-3
>100
2
3.6 ∙ 10-3
+0.95 pA 14.03.2018
23.0
0.5
1000
15
45
10
0.950827·10-12
1
-0.951753·10-12
1.000974
2.5 ∙ 10-4
>100
2
5.0 ∙ 10-4
-0.95 pA
14.03.2018
23.0
0.5
1000
15
45
10
-0.950821·10-12
1
0.951745·10-12
1.000972
2.5 ∙ 10-4
>100
2
5.0 ∙ 10-4
+9.5 pA
14.03.2018
23.0
0.5
1000
15
45
10
9.49910·10-12
10
-9.50842·10-12
1.000981
0.6∙ 10-4
>100
2
1.2 ∙ 10-4
-9.5 pA
14.03.2018
23.0
0.5
1000
15
45
10
-9.49908·10-12
10
9.50736·10-12
1.000872
0.6∙ 10-4
>100
2
1.2 ∙ 10-4
+95 pA
14.03.2018
23.0
0.5
1000
15
45
10
94.9990·10-12
100
-95.0251·10-12
1.000274
2.5∙ 10-5
>100
2
5.0 ∙ 10-5
-95 pA
14.03.2018
23.0
0.5
1000
15
45
10
-94.9986·10-12
100
95.0216·10-12
1.000242
2.5∙ 10-5
>100
2
5.0 ∙ 10-5
66
LNE
U
Temp.
Nom.
Current
(Temp.)
Press.
)
( °C
Humid.
(Press.)
Date
( °C
U
(mbar)
)
(mbar)
U
(Humid.)
(%rh)
(%rh)
Supplied
Current
(A)
Transfer
instrument’s
measuring
range
Reading of
transfer
instrument
( pA )
(A)
Standard
uncertainty
Ratio
of
(Measurement
Degrees
measurement
result)
of
(combined
freedom
type A and B)
Q
U
k
(k·u(Q))
u(Q)
+9.5 fA
18.04.2018
23
0.5
1015
15
45
5
9.5027·10-15
1
9.5863·10-15
1.0088
3.74·10-2
>500
2
7.48·10-2
-9.5 fA
18.04.2018
23
0.5
1015
15
45
5
-9.4719·10-15
1
-9.4918·10-15
1.0021
3.48·10-2
>500
2
6.96·10-2
+95 fA
22.04.2018
23
0.5
1015
15
45
5
94.916·10-15
1
95.274·10-15
1.0038
4.58·10-3
>500
2
9.16·10-3
-95 fA
22.04.2018
23
0.5
1015
15
45
5
-94.957·10-15
1
-95.184·10-15
1.0024
4.70·10-3
>500
2
9.40·10-3
+0.95 pA 26.04.2018
23
0.5
1015
15
45
5
0.94671·10-12
1
0.94945·10-12
1.0029
4.44·10-4
>500
2
8.88·10-4
-0.95 pA
26.04.2018
23
0.5
1015
15
45
5
-0.94674·10-12
1
-0.94938·10-12
1.0028
4.25·10-4
>500
2
8.50·10-4
+9.5 pA
01.05.2018
23
0.5
1015
15
45
5
9.4654·10-12
10
9.4790·10-12
1.00143
10.7·10-5
>500
2
21.4·10-5
-9.5 pA
01.05.2018
23
0.5
1015
15
45
5
-9.4652·10-12
10
-9.4775·10-12
1.00130
10.8·10-5
>500
2
21.6·10-5
+95 pA
03.05.2018
23
0.5
1015
15
45
5
94.927·10-12
100
94.966·10-12
1.00041
4.76·10-5
>500
2
9.5·10-5
-95 pA
03.05.2018
23
0.5
1015
15
45
5
-94.930·10-12
100
-94.964·10-12
1.00036
4.78·10-5
>500
2
9.6·10-5
67
NSAI
U
Temp.
Nom.
Current
(Temp.)
Press.
)
( °C
Humid.
(Press.)
Date
( °C
U
(mbar)
)
(mbar)
U
(Humid.)
(%rh)
(%rh)
Supplied
Current
(A)
Transfer
instrument’s
measuring
range
Reading of
transfer
instrument
( pA )
(A)
Standard
uncertainty
Ratio
of
(Measurement
Degrees
measurement
result)
of
(combined
freedom
type A and B)
Q
U
k
(k·u(Q))
u(Q)
+9.5 fA
15.06.2018
23.2
0.1
1012
4
40
4
9.514·10-15
1
-9.536·10-15
1.0023
0.017
>104
2
0.034
-9.5 fA
15.06.2018
23.2
0.1
1012
4
40
4
-9.511·10-15
1
9.538·10-15
1.0028
0.017
>104
2
0.034
+95 fA
12.06.2018
23.2
0.1
1010
4
39
4
95.140·10-15
1
-95.400·10-15
1.0027
0.0021
349
2
0.0042
-95 fA
12.06.2018
23.2
0.1
1010
4
39
4
-95.106·10-15
1
95.362·10-15
1.0027
0.0021
349
2
0.0042
+0.95 pA 11.06.2018
23.2
0.1
1012
4
39
4
0.95167·10-12
1
-0.95421·10-12
1.00267
0.00028
50
2.05
0.00057
-0.95 pA
11.06.2018
23.2
0.1
1012
4
39
4
-0.95124·10-12
1
0.95369·10-12
1.00257
0.00028
50
2.05
0.00057
+9.5 pA
11.06.2018
23.3
0.1
1011
4
40
4
9.5174·10-12
10
-9.5313·10-12
1.00146
0.00016
105
2
0.00032
-9.5 pA
11.06.2018
23.3
0.1
1011
4
40
4
-9.5131·10-12
10
9.5262·10-12
1.00138
0.00016
105
2
0.00032
+95 pA
12.6.2018
23.3
0.1
1011
4
41
4
95.1819·10-12
100
-95.2233·10-12
1.00044
0.00014
292
2
0.00028
-95 pA
12.6.2018
23.3
0.1
1011
4
41
4
-95.1391·10-12
100
95.1769·10-12
1.00040
0.00014
292
2
0.00028
68
METAS
U
Temp.
Nom.
Current
(Temp.)
Press.
)
( °C
Humid.
(Press.)
Date
( °C
U
(mbar)
)
(mbar)
U
(Humid.)
(%rh)
(%rh)
Supplied
Current
(A)
Transfer
instrument’s
measuring
range
Reading of
transfer
instrument
( pA )
(A)
Standard
uncertainty
Ratio
of
(Measurement
Degrees
measurement
result)
of
(combined
freedom
type A and B)
Q
U
k
(k·u(Q))
u(Q)
+9.5 fA
20.09.2018
22.8
0.5
960
5
50
5
9.50038·10-15
1
9.52645·10-15
1.00274
0.0026
57
2.04
0,0053
-9.5 fA
20.09.2018
22.8
0.5
960
5
50
5
-9.50041·10-15
1
9.52415·10-15
1.0025
0.00287
57
2.04
0,00586
+95 fA
18.09.2018
22.9
0.5
960
5
50
5
95.0043·10-15
1
95.2309·10-15
1.00239
0.00058
38
2.07
0,00120
-95 fA
18.09.2018
22.9
0.5
960
5
50
5
-95.0041·10-15
1
-95.2163·10-15
1.00223
0.00059
38
2.07
0,00122
+0.95 pA 18.09.2018
22.9
0.5
962
5
48
5
0.950039·10-12
1
0.952278·10-12
1.002357
0.000061
54
2.05 0,000125
-0.95 pA
18.09.2018
22.9
0.5
962
5
48
5
-0.950036·10-12
1
-0.952082·10-12
1.002154
0.000061
55
2.05 0,000125
+9.5 pA
18.09.2018
22.9
0.5
965
5
48
5
9.50041·10-12
10
9.51307·10-12
1.001333
0.000028
84
2.03 0,000057
-9.5 pA
18.09.2018
22,9
0.5
965
5
48
5
-9.50039·10-12
10
-9.51160·10-12
1.001180
0.000028
82
2.03 0,000057
+95 pA
18.09.2018
22.8
0.5
960
5
50
5
95.0073·10-12
100
95.0496·10-12
1.000445
0.000021
69
2.04 0,000043
-95 pA
18.09.2018
23.0
0.5
964
5
48
5
-95.0070·10-12
100
-95.0421·10-12
1.000369
0.000023
85
2.03 0,000047
69
HU-BFKH
U
Temp.
Nom.
Current
(Temp.)
Press.
)
( °C
Humid.
(Press.)
Date
( °C
U
(mbar)
)
(mbar)
U
(Humid.)
(%rh)
(%rh)
Supplied
Current
(A)
Transfer
instrument’s
measuring
range
Reading of
transfer
instrument
( pA )
(A)
Standard
uncertainty
Ratio
of
(Measurement
Degrees
measurement
result)
of
(combined
freedom
type A and B)
Q
U
k
(k·u(Q))
u(Q)
-
-
-
-
-
-
-
-
-
-
-
-
-
0.44
999.6
1.4
43.8
6.2
-10.197·10-15
1
-9.557·10-15
0.93727
57.8·10-3
60600
2
116·10-3
-
-
-
-
-
-
-
-
-
-
-
-
-
07.11.2018 22.66
0.44
999.6
1.4
43.8
6.2
-95.030·10-15
1
-95.058·10-15
1.000294
5.78·10-3
74800
2
11.6·10-3
+0.95 pA 22.10.2018 22.47
0.28
8.7
44.9
5.4
0.94803·10-12
1
0.94737·10-12
0.999299
581·10-6
>105
2
116·10-5
-0.95 pA
22.10.2018 22.47
0.28
8.7
44.9
5.4
-0.95214·10-12
1
-0.95597·10-12
1.004027
581·10-6
>105
2
116·10-5
+9.5 pA
22.10.2018 22.47
0.28
8.7
44.9
5.4
9.48944·10-12
10
9.49589·10-12
1.000679
73·10-6
3480
2
146·10-6
-9.5 pA
22.10.2018 22.47
0.28
8.7
44.9
5.4
-9.49539·10-12
10
-9.50599·10-12
1.001117
73·10-6
3480
2
146·10-6
+95 pA
18.10.2018 22.56
0.22
999.3
2.6
44.0
2.7
94.9507·10-12
100
94.9973·10-12
1.000490
33·10-6
168
2
66·10-6
-95 pA
18.10.2018 22.56
0.22
999.3
2.6
44.0
2.7
-94.9633·10-12
100
-95.0091·10-12
1.000482
33·10-6
168
2
66·10-6
+9.5 fA*
-9.5 fA
+95 fA*
-95 fA
-
-
07.11.2018 22.66
-
-
1000.
6
1000.
6
1000.
6
1000.
6
*: HU-BFKH did not declare +95 fA and +9.5 fA results
70
RISE
U
Temp.
Nom.
Current
(Temp.)
Press.
)
( °C
Humid.
(Press.)
Date
( °C
U
(mbar)
)
(mbar)
U
(Humid.)
(%rh)
(%rh)
Supplied
Current
( A )*
Transfer
instrument’s
measuring
range
Reading of
transfer
instrument
( pA )
( A )*
Standard
uncertainty
Ratio
of
(Measurement
Degrees
measurement
result)
of
(combined
freedom
type A and B)
Q
U
k
(k·u(Q))
u(Q)
+9.5 fA
16.11.2018
23
1
1020
10
45
10
9.5·10-15
1
-
0.9994
0.0035
10
2.28
0,0080
-9.5 fA
16.11.2018
23
1
1020
10
45
10
-9.5·10-15
1
-
1.0011
0.0035
10
2.28
0,0080
+95 fA
15.11.2018
23
1
1020
10
45
10
95·10-15
1
-
1.00279
0.00030
10
2.28
0,00069
-95 fA
15.11.2018
23
1
1020
10
45
10
-95·10-15
1
-
0.99967
0.00030
10
2.28
0,00069
+0.95 pA 19.11.2018
23
1
1020
10
45
10
0.95·10-12
1
-
1.002030
0.000029
7
2.43 0,000070
-0.95 pA
19.11.2018
23
1
1020
10
45
10
-0.95·10-12
1
-
1.001978
0.000029
7
2.43 0,000070
+9.5 pA
20.11.2018
23
1
1020
10
45
10
9.5·10-12
10
-
1.001313
0.000033
9
2.32 0,000077
-9.5 pA
20.11.2018
23
1
1020
10
45
10
-9.5·10-12
10
-
1.001259
0.000033
9
2.32 0,000077
+95 pA
21.11.2018
23
1
1020
10
45
10
95·10-12
100
-
1.000487
0.000026
5
2.65 0,000069
-95 pA
21.11.2018
23
1
1020
10
45
10
-95·10-12
100
-
1.000457
0.000026
5
2.65 0,000069
*: RISE declared only Q (Ratio) values
71
IPQ
Nom.
Current
U
Date
U
Temp.
Press.
(Temp.)
( °C)
( °C
)
(Humid.)
Supplied
Current
Transfer
instrument’s
measuring
range
Reading of
transfer
instrument
U
Humid.
(Press.)
Standard
uncertainty
Ratio
Degrees
of
(Measurement
of
measurement
result)
freedom
(combined
type A and B)
(mbar)
(mbar)
(%rh)
(%rh)
(A)
(pA)
(A)
Q
u(Q)
k
U
(k·u(Q))
+9.5 fA
14.06.2019
23.3
0.3
1003.9
0.2
53
3
-
1
-
0.967
0.132
>100
2
0.264
-9.5 fA
13.06.2019
23.3
0.3
1004.1
0.2
52
3
-
1
-
1.018
0.101
>100
2
0.202
+95 fA
12.06.2019
23.4
0.3
1005.2
0.2
56
3
-
1
-
0.9981
0.0166
>100
2
0.0332
-95 fA
13.06.2019
23.5
0.3
1004.8
0.2
56
3
-
1
-
1.0150
0.0087
>100
2
0.0174
+0.95 pA*
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-0.95 pA
14.06.2019
23.3
0.3
1002.8
0.2
52
3
-
1
-
1.0000
0.0017
>100
2
0.0034
+9.5 pA
09.06.2019
23.5
0.3
1003.6
0.2
50
3
-
10
-
1.00088
0.00081
>100
2
0.00162
-9.5 pA
05.06.2019
23.4
0.3
1006.0
0.2
51
3
-
10
-
1.00000
0.00070
>100
2
0.00140
+95 pA
03.06.2019
23.1
0.3
1008.4
0.2
55
3
-
100
-
1.00079
0.00120
>100
2
0.00240
-95 pA
05.06.2019
23.2
0.3
1008.0
0.2
53
3
-
100
-
1.00020
0.00072
>100
2
0.00144
*: IPQ did not declare +0.95 pA results
72
Appendix B: Uncertainty Budgets of the participants
During this comparison, 8 participants, each measured 5 current values and 2 current directions
were performed giving 80 results and also 80 uncertainty budgets. It is not reasonable to present
such a large number of uncertainty budgets in this report. Instead, for each participant only two
uncertainty budgets will be presented, at the current values +95 fA and +95 pA. This choice was
made because these current values are at the extremes and because the same choice was made in
EURAMET.EM-S24.
Uncertainty Budgets of TÜBİTAK UME (pilot institute)
Model function
:𝑸
Nominal Current
: 95 pA
Quantity
6430 Meas. Std. Dev
Imeas
6430 Meas. Res.
δIres
3458A Certificate
Vcal
3458A Drift
δVdrf
Resistance Certificate
Rcal
Resistance Drift
δRdrf
Res. Temp. Coeff.
δRtemp
6430 Appl. Std. Dev.
Iappl
6430 Q Std. Dev.
Q
=
( I meas   I res )
( Vcal   Vdrf ) ( Rcal   Rdrf   Rtemp )
Standard
Uncertainty
u(xi)
Distribution
Function
Sensitivity
Coefficient
ci
95 pA
3.0 ∙ 10-16 A
Normal, k=1
1.0 ∙ 1010 Ω/V
3.0 ∙ 10-6
>100
0
5.0 ∙ 10-17 A
Rectangular
1.0 ∙ 1010 Ω/V
2.9 ∙ 10-7
∞
1.0 ∙ 10-6
∞
4.62 ∙ 10-6
∞
-1.0 ∙
Ω·A/V2
-1.0 ∙ 101
Ω·A/V2
101
0.1 V
2.0 ∙ 10-7 V
Normal, k=2
0
8.0 ∙ 10-7 V
Rectangular
1 GΩ
1.2 ∙ 104 Ω
Normal, k=2
1.0 ∙ 10-9 A/V
6.0 ∙ 10-6
∞
0
1.0 ∙ 104 Ω
Rectangular
1.0 ∙ 10-9 A/V
5.77 ∙ 10-6
∞
0
1.0 ∙ 104 Ω
Rectangular
1.0 ∙ 10-9 A/V
5.77 ∙ 10-6
∞
95 pA
2.5 ∙ 10-16 A
Normal, k=1
-1.0 ∙ 1010 1/A
2.5 ∙ 10-6
>100
1
2.2 ∙ 10-5
Normal, k=1
1
2.2 ∙ 10-5
>100
Combined Uncertainty
2.5 ∙ 10-5
eff > 100
Expanded Uncertainty (%95.5)
5.0 ∙ 10-5
Q+
1.000274
Calibration Factor
Uncertainty Degrees
of
contribution
freedom
u(yi)=
ci .u(xi)
i
Expected
Value
xi
Q1.000242
73
=
𝑰𝒎𝒆𝒂𝒔
Model function
:𝑸
Nominal Current
: 9.5 fA
(𝑪𝒔𝒆𝒓 + 𝑪𝑨𝑪−𝑫𝑪 ) ∙ 𝒅𝑽⁄
𝒅𝒕
Quantity
Expected
Value
xi
Standard
Uncertainty
u(xi)
Distribution
Function
Cap. Certificate
Cser
1 pF
2.0 ∙ 10-17 F
Normal, k=2
Cap. AC-DC
Difference
CAC-DC
0
3.0 ∙ 10-16 F
Normal, k=2
Ramp Voltage
dV/dt
9.5 mV/s
2.0 ∙ 10-6 V/s
Normal, k=2
6430 Measurement
Std. Dev.
Imeas
9.5 fA
1.8 ∙ 10-16 A
Normal, k=1
Q Std. Dev.
Q
1
2.2 ∙ 10-3
Normal, k=1
Q+
1.0049
Calibration Factor
Q0. 9957
Sensitivity
Coefficient
ci
-1.0 ∙ 1012
A/(F2 ∙ (V/s))
-1.0 ∙ 1012
A/(F2 ∙ (V/s))
-1.0 ∙ 102
A/(F ∙ (V/s)2)
1.0 ∙ 1014
1/A
1
Uncertainty
contribution
u(yi)=
ci .u(xi)
Degree of
freedom
i
1.0 ∙ 10-5
∞
1.5 ∙ 10-4
>100
1.0 ∙ 10-4
>100
1.8 ∙ 10-2
>100
2.2 ∙ 10-3
>100
Combined Uncertainty
1.8 ∙ 10-2
Expanded Uncertainty (%95.5)
3.6 ∙ 10
eff >100
-2
For 95 pA and 9.5 pA current method of generating the calibrating current by a voltage source and a
resistor was used.
For 0.95 pA, 95 fA and 9.5 fA current values the method of generating the calibrating current by
charging/discharging a capacitor was used.
Uncertainty Budgets of LNE
74
The quantity reported as the result of the travelling standard calibration is the ratio, noted in this
report as Q, between the reading of travelling standard, IR, and the supplied DC current, IS.
𝐼𝑅
𝐼𝑆
𝑄=
Final result, 𝑄𝐹 ,
(1)
𝑢𝑐 (𝑄𝐹 ).
For each nominal current, the final value of the ratio, QF, is calculated as the weighted mean of the
values provided by the used methods:
𝑄𝐹 =
𝑚𝑒𝑡
∑𝑁
𝑖=1
𝑄𝑚𝑒𝑡 𝑖
2
𝑢 (𝑄𝑚𝑒𝑡 𝑖 )
𝑚𝑒𝑡
∑𝑁
𝑖=1
1
𝑢2 (𝑄𝑚𝑒𝑡 𝑖 )
(2)
With



Nmet : The number of the used methods for one nominal current (usually 3 except for the ± 95 pA
which is the result of several repetitions of only one method);
𝑄 𝑚𝑒𝑡 𝑖 : The ratio obtained with the method i
𝑢(𝑄𝑚𝑒𝑡 𝑖 ) : The combined standard uncertainty of the ratio obtained with the method i
The Equation 2 can be written also as:
𝑄𝐹 = ∑
𝑁𝑚𝑒𝑡
𝑖=1
µ𝑖 𝑄𝑚𝑒𝑡,𝑖
with µi – the weight associated to the method i and computed according to the Equation 3:
1
𝑢2 (𝑄𝑚𝑒𝑡,𝑖 )
µ𝑖 =
1
𝑚𝑒𝑡
∑𝑁
𝑖=1 𝑢 2 (𝑄
𝑚𝑒𝑡,𝑖 )
(3)
The combined uncertainty of the final value of the ratio, uc(QF), is obtained by applying the law of
propagation of uncertainties and considering the full correlation between the used methods. This
uncertainty is given by the Equation 4:
𝑢𝑐 (𝑄𝐹 ) = ∑
𝑁𝑚𝑒𝑡
𝑖=1
µ𝑖 𝑢( 𝑄𝑚𝑒𝑡,𝑖 )
(4)
75
Result of several repetitions of one method, 𝑄𝑚𝑒𝑡,𝑖 ;
𝑢(𝑄𝑚𝑒𝑡,𝑖 )
Let’s name the result of one calibration Qj with 𝑄𝑗 =
𝐼𝑅,𝑗
𝐼𝑆,𝑗
the ratio between the reading of the
travelling standard, IR,j and the supplied current, IS,j; j varying from 1 to k (the total number of
repetitions of one method). The ratio obtained with the method i is the average of the ratios after
repeating k times the same method i. The Equation 5 is applied:
𝑄𝑚𝑒𝑡,𝑖 =
𝑘
1
∑ 𝑄𝑗
𝑘
𝑗=1
(5)
The combined standard uncertainty related to 𝑄𝑚𝑒𝑡,𝑖 is computed according to the equation 6:
𝑢(𝑄𝑚𝑒𝑡,𝑖 ) = √𝑢𝐴2 (𝑄𝑚𝑒𝑡,𝑖 ) + 𝑢𝐵2 (𝑄𝑚𝑒𝑡,𝑖 )
(6)
Where:
𝑢𝐴 (𝑄𝑚𝑒𝑡,𝑖 ) =
𝑢𝐵 (𝑄𝑚𝑒𝑡 𝑖 ) = √
𝑆𝑡𝐷𝑒𝑣(𝑄𝑗 )
√𝑘
∑𝑘𝑗=1(𝑛𝑗 − 1)𝑢2 (𝑄𝑗 )
(∑𝑘𝑗=1 𝑛𝑗 − 𝑘)
(7)
(8)
nj is the degree of freedom related to the j calibration.
Result of one calibration, 𝑄𝑗 ;
𝑢(𝑄𝑗 )
For the measurement j, the result is 𝑄𝑗 =
𝐼𝑅,𝑗
𝐼𝑆,𝑗
, the ratio between the corrected value of the travelling
standard reading, 𝐼𝑅,𝑗 and the supplied current, 𝐼𝑆,𝑗 .
The law of uncertainties propagation leads to the relative standard uncertainty given by the equation
9:
𝑢𝑟 (𝑄𝑗 ) = √𝑢𝑟2 (𝐼𝑅,𝑗 ) + 𝑢𝑟2 (𝐼𝑆,𝑗 )

𝑢𝑟 (𝐼𝑅,𝑗 ) =
𝑢(𝐼𝑅,𝑗 )
𝐼𝑅,𝑗
(9)
is the relative standard uncertainty related to the corrected reading of the
travelling standard;

𝑢𝑟 (𝐼𝑆,𝑗 ) =
𝑢(𝐼𝑆,𝑗 )
𝐼𝑆,𝑗
is the relative standard uncertainty of the supplied current.
The absolute value of the standard uncertainty of the ratio Qj can be obtained by: 𝑢(𝑄𝑗 ) = 𝑄𝑗 𝑢𝑟 (𝑄𝑗 ).
The components and their associated uncertainties are detailed in the followings.
76
Readings of the current by the travelling standard, 𝐼𝑅,𝑗
For one measurement, j, the corrected reading of the travelling standard is obtained according to the
equation 10 as the mean value of the 1001 acquisitions, IAcquired,j minus the zero level, Izero (mean
value of 1001 acquisitions).
𝑰𝑹,𝒋 = −(𝑰𝑨𝒄𝒒𝒖𝒊𝒓𝒆𝒅,𝒋 − 𝑰𝒛𝒆𝒓𝒐,𝒋 )
(10)
The minus sign in front of the brackets corresponds to the explanation given in the Annex of the
technical protocol: “Nevertheless, with respect to the comparison currents flowing into the instrument
are to be counted positive and currents flowing out of the instrument are to be counted negative.
Therefore, the displayed current values must be multiplied by a factor of -1.”
Standard uncertainty related to the corrected reading of the travelling standard, 𝒖𝒓 (𝑰𝑹,𝒊 )
Based on the Equation 10, the relative value of the standard uncertainty (k =1) is given by:
𝒖𝒓 (𝑰𝑹,𝒋 ) =
𝟏
√𝒖𝟐𝑨 (𝑰𝑨𝒄𝒒𝒖𝒊𝒓𝒆𝒅,𝒋 ) + 𝒖𝟐𝑨 (𝑰𝒛𝒆𝒓𝒐,𝒋 ) + 𝟐𝒖𝟐𝒓𝒆𝒔 (𝑰𝑨𝒄𝒒𝒖𝒊𝒓𝒆𝒅,𝒊 )
𝑰𝑹,𝒋
(11)
where:



𝑢𝐴 (𝐼𝐴𝑐𝑞𝑢𝑖𝑟𝑒𝑑,𝑗) is the standard deviation of the 1001 acquisitions of the readings of the current
measured by the travelling standard;
𝑢𝐴 (𝐼𝑧𝑒𝑟𝑜,𝑗 ) is the standard deviation of the 1001 acquisitions of the readings of the travelling
standard in the configuration of zero level determination;
𝑢𝑟𝑒𝑠 (𝐼𝐴𝑐𝑞𝑢𝑖𝑟𝑒𝑑,𝑗 ) =
𝑅𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝐵𝑦 𝑟𝑎𝑛𝑔𝑒
2√3
is the uncertainty related to the resolution of the travelling
standard. The value of the 𝑅𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝐵𝑦 𝑟𝑎𝑛𝑔𝑒 depends on the current measurement range of
the device; a rectangular distribution law is associated to this component. This component is
considered twice since it contributes both to the zero level and current level determination.
Supplied current, 𝐼𝑆,𝑗
(1) Voltage-resistor method
𝑰𝑺,𝒋 =
𝑽
𝑹
(12)
Where
V : represents the DC voltage provided by the stable generator;
R : is the resistance of the high value resistor.
77
Standard uncertainty related to the supplied current by voltage-resistor method, 𝒖𝒓 (𝑰𝑺,𝒋 )
The propagation law of the uncertainties leads to:
𝒖𝒓 (𝑰𝑺,𝒋 ) =
𝒖(𝑰𝑺,𝒋 )
𝒖𝟐 (𝑽) 𝒖𝟐 (𝑹)
=√ 𝟐 +
𝑰𝑺,𝒋
𝑽
𝑹𝟐
(13)
The uncertainty components related to the generated DC voltage are:
𝒖(𝑽) = √𝒖𝟐𝑪𝒂𝒍 (𝑽) + 𝒖𝟐𝑫𝒓𝒊𝒇𝒕 (𝑽) + 𝒖𝟐𝑻𝒆𝒎𝒑 (𝑽)
(14)
with:

𝑢𝐶𝑎𝑙 (𝑉)- the standard uncertainty coming from the calibration certificate where it is expressed
in terms of expanded uncertainty with a coverage factor k = 2. Therefore, the component is
calculated with the formula:
1
𝑢𝐶𝑎𝑙 (𝑉) = 2 (1.0 ∙ 10−5 ∙ 𝑉 + 0.1 µ𝑉); V being the generated voltage

𝑢𝐷𝑟𝑖𝑓𝑡 (𝑉) – the standard uncertainty due to the drift of the calibrator over one week. This
component is estimated as explained in the following. The correction of the calibrator on the
used range is followed over the last 10 years (2008 -2018). The maximum difference
between 2 consecutive years gives the drift over 1 year and the value corresponding to one
week is, then, determined. A rectangular distribution law is associated with this drift.
𝑢𝐷𝑟𝑖𝑓𝑡 (𝑉) =

𝑀𝑎𝑥(𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛𝑦+1 −𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛𝑦 )/52
;
2√3
𝑢 𝑇𝑒𝑚𝑝 (𝑉)- the standard uncertainty related to the influence of the variation of the room
temperature. The measurement environment was temperature regulated; therefore, a
derived arcsine distribution law is associated to this variation.
𝛼𝐶𝑎𝑙𝑖𝑏𝑟𝑎𝑡𝑜𝑟 ∙ ∆𝑇 ∙ 𝑉
𝑢 𝑇𝑒𝑚𝑝 (𝑉) =
√2
Temperature coefficients for Datron 4808 DC voltage generator
Range
100 mV
1V
10 V
Temperature
coefficient (ppm/°C)
±1
±0.5
±0.15
78
The uncertainty components related to the high value resistor are:
𝒖(𝑹) = √𝒖𝟐𝑪𝒂𝒍 (𝑹) + 𝒖𝟐𝑻𝒆𝒎𝒑 (𝑹) + 𝒖𝟐𝑰𝒏𝒕𝒆𝒓𝒑𝒐𝒍𝒂𝒕𝒊𝒐𝒏,𝑽 (𝑹)
(15)
with:


𝑢𝐶𝑎𝑙 (𝑅) : The standard uncertainty coming from the calibration certificate where it is
expressed in terms of expanded uncertainty with a coverage factor k = 2. Therefore, the
component is calculated according to the formulas:
Value of R
Standard uncertainty from calibration (k = 1)
10 TΩ
1
𝑢𝐶𝑎𝑙 (𝑅) = √4 ∙ 103 + 11 ∙ 10−20 /𝐼2 ∙ 10−6 ∙ 𝑅
2
1 TΩ; 100 GΩ
1
𝑢𝐶𝑎𝑙 (𝑅) = √1 ∙ 103 + 11 ∙ 10−20 /𝐼2 ∙ 10−6 ∙ 𝑅
2
𝑢 𝑇𝑒𝑚𝑝 (𝑅) : The standard uncertainty related to the influence of the variation of the room
temperature. The measurement environment was temperature regulated; therefore, a
derived arcsine distribution law is associated to this variation.
𝑢 𝑇𝑒𝑚𝑝 (𝑅) =

𝛼𝑅 ∙∆𝑇∙𝑅
,
√2
𝛼𝑅 = 200 𝑝𝑝𝑚/°𝐶
𝑢𝐼𝑛𝑡𝑒𝑟𝑝𝑜𝑙𝑎𝑡𝑖𝑜𝑛,𝑉 (𝑅) : The standard uncertainty related to the voltage interpolation. The high
value resistors were calibrated under two voltages framing the measurement voltage. A
linear variation between the calibrated points was considered, knowing that the resistor was
used for a very low power (less than 1% of its nominal value). The interpolation uncertainty is
obtained by applying the law of propagation of uncertainties following the relationship
between resistance measurements and their uncertainties.
(2) Sub-Femtoamp Current source
Some of the measurements were performed using the LNE Sub-Femtoamp source type Keithley
6430 and its preamplifier. This current source was used to calibrate the travelling standard and
immediately after, the LNE Sub-Femtoamp source was calibrated at the same current as before
using the integration bridge.
Therefore, the standard uncertainty related to the supplied current by this method, 𝒖𝒓 (𝑰𝑺,𝒋 ) is
composed of :
𝒖𝒓 (𝑰𝑺,𝒋 ) =
𝒖(𝑰𝑺,𝒋 )
𝟏
=
√𝒖𝟐𝑪𝒂𝒍 (𝑰𝑺,𝒋 ) + 𝒖𝟐𝒅𝒓𝒊𝒇𝒕,𝟏𝒘𝒌 (𝑰𝑺,𝒋 )
𝑰𝑺,𝒋
𝑰𝑺,𝒋
(16)
79
with:


𝑢𝐶𝑎𝑙 (𝐼𝑆,𝑗 ) - the standard uncertainty coming from the calibration certificate. The uncertainty
associated to the LNE integration bridge is given in terms of expanded uncertainty with a
coverage factor of k = 2. Therefore, the standard uncertainty component is given by the
1
following formula : 𝑢𝐶𝑎𝑙 (𝐼𝑆,𝑖 ) = 2 (4.7 ∙ 10−5 ∙ 𝐼𝑆,𝑗 + 0.3 𝑓𝐴)
𝑢𝑑𝑟𝑖𝑓𝑡,1𝑤𝑘 (𝐼𝑆,𝑗 ) - the standard uncertainty due to the drift of the LNE current source over one
week. This component is estimated on the basis of the manufacturer data that are briefly
reminded in the following table and divided by 52 to get the drift over 1 week:
Range of 6430
Accuracy (23°C ± 5°C) 1 Year
±(%rdg + amps)
1 pA
1% ∙ 𝐼𝑆,𝑗 + 7 𝑓𝐴
10 pA
0.5% ∙ 𝐼𝑆,𝑗 + 7 𝑓𝐴
100 pA
0.15% ∙ 𝐼𝑆,𝑗 + 30 𝑓𝐴
The influence of the stability and the resolution on the measurements are taken into account through
the standard deviation of the readings and of the zero level before and after the measurements.
Numerical examples of uncertainty budget calculations are given in the following for +9.5 fA.
Table 21. Uncertainty budget for Reading 1 of the current (IR,1 , 𝒖𝒓 (𝑰𝑹,𝟏 ))
Quantity
Expected
Value
xi
Standard
Uncertainty
u(xi)
Uncertainty
Type
Sensitivity
Coefficient
ci
Uncertainty
contribution
ur(yi)
Stability of Reading
-9,740E-15
3,807E-16
A
1
3,807E-16
Stability of Zero
-5,200E-17
5,528E-16
A
1
5,528E-16
Resolution of
Travelling Standard
1,00E-17
2,89E-18
B
1
2,89E-18
Corrected
Reading, IR,i
9,688E-15
Combined Uncertainty for IR,i
2,24E-16
Both type A uncertainties represent the highest contributions to the final 𝑢(𝑄𝑗 ) uncertainty. There
are several measurements repeated and independent. Therefore the type A uncertainties are
divided by the root of the number of repetitions. It is not the case for the component resulting from
the resolution.
80
Table 22. Uncertainty budget for supplied current,
Sub-Femtoamp Current source (IS,1 , 𝒖𝒓 (𝑰𝑺,𝟏 )), Method 1
Expected Value
xi
Standard
Uncertainty
u(xi)
Uncertainty
Type
Sensitivity
Coefficient
ci
Uncertainty
contribution
ur(yi)
Calibration
-
1,50E-16
B
1
1,50E-16
Drift,1 week
-
1,36E-16
B
1
1,36E-16
Supplied
current, IS,1
9,487E-15
Quantity
Combined Uncertainty for IS,i
2,03E-16
Table 23. Uncertainty budget for supplied current,
Voltage-resistor method, (IS,4 , 𝒖𝒓 (𝑰𝑺,𝟒 )), Method 2
Standard
Uncertainty
u(xi)
Uncertainty
Type
Sensitivity
Coefficient
ci
Uncertainty
contribution
ur(yi)
Calibration
9,75E-08
B
1
9,75E-08
Drift, 1 week
1,11E-08
B
1
1,11E-08
Temperature
3,36E-08
B
1
3,36E-08
Quantity
Voltage
Expected
Value
xi
0,0095
Combined Uncertainty for V (V)
Resistor
1,04E-07
9,97E+11
Calibration
1,73E+10
B
1
1,73E+10
Temperature
7,05E+07
B
1
7,05E+07
Voltage
interpolation
3,97E+07
B
1
3,97E+07
Combined Uncertainty for R (Ω)
1,73E+10
Combined Relative Uncertainty for IS,i (A/A)
1,74E-02
Supplied
current IS,4
9,5329E-15
81
Table 24. Uncertainty budget for the ratios for the nominal current: + 9.5 fA
Corrected
Reading,
Relative
standard
uncertainty,
Supplied
Current,
Relative
standard
uncertainty,
Ratio
Relative
Standard
Uncertainty
IR,j (A)
ur(IR,j)(A/A)
IS,j (A)
ur(IS,j)(A/A)
9,688E-15
2,31E-02
9,487E-15
2,14E-02
1,0212
3,15E-02
3,21E-02
522
9,440E-15
2,25E-02
9,487E-15
2,14E-02
0,9951
3,10E-02
3,09E-02
522
9,274E-15
2,47E-02
9,487E-15
2,14E-02
0,9776
3,27E-02
3,19E-02
523
9,820E-15
3,65E-02
9,533E-15
1,74E-02
1,0301
4,04E-02
4,17E-02
529
9,735E-15
3,83E-02
9,533E-15
1,74E-02
1,0212
4,21E-02
4,30E-02
530
Method
Met 1
LNE
Sub-Femt.
Source
Met 2
U/1 TΩ
Standard
Effective
Uncertainty Degrees
of
of
Measurement Freedom
The degrees of freedom in the Table 16 are determined according to the formula (G.2b) of the
Annex G of GUM [2]:
𝐷𝑜𝐹𝑖 =
𝑢4 (𝑄𝑖 )
𝑢4 (𝐼𝐴𝑐𝑞𝑢𝑖𝑟𝑒𝑑,𝑖 ) 𝑢4 (𝐼𝑂𝑓𝑓,𝑖 )
+
1000
1000
(17)
Table 25. Weighted mean value and its uncertainty (Equation 2 and 3)
Method
Met1
Met2
Ratio per
method
Standard
Uncertainty
(Pooled
variance)
StDev
/root(k)
Standard
uncertainty of
measurement
(A/A)
(Type B)
(Type A)
(Combined
Type A and B)
0,9980
3,16E-02
1,27E-02
3,41E-02
1,0257
4,23E-02
4,46E-03
4,26E-02
Weight for
methods
Ratio
Final
value
Combined
Standard
Uncertainty
(A/A)
k=1
1,0088
3,74E-02
6,09E-01
3,91E-01
82
Uncertainty Budget of NSAI
Model function
:𝑸=
−(𝑿−𝑿𝟎 )
(𝑰𝑿 −𝑰𝟎 )
where 𝑿 and 𝑿𝟎 are the electrometer readings corresponding to the nominal input test current 𝑰𝑿
and nominal zero input current 𝑰𝒐
𝑰𝑿 =
where
∆𝑽𝑿
∆𝒕𝑺
∆𝑽𝑿
∆𝒕𝑺
∙ 𝑪 + 𝑰𝑷 + 𝑰𝑳 ,
is the slope of the voltage ramp calculated from successive readings of the sampling
multimeter (∆𝐕𝑿 = 𝑽𝒋+𝟏 − 𝑽𝒋 ) and the sample time interval ∆𝒕𝑺 ,𝑪 is the value of the gas filled
capacitor at DC, 𝑰𝑷 is the leakage current at the input terminal of the capacitor, and 𝑰𝑳 is the
leakage current at the input terminal of the electrometer during the ramp portion of the measurement
cycle
Similarly
𝑰𝟎 =
∆𝑽𝟎
∆𝒕𝑺
∙ 𝑪 + 𝑰′𝑷 + 𝑰′𝑳
where 𝑰′𝑷 is the leakage current at the input terminal of the capacitor, and 𝑰′𝑳 is the leakage current
at the input terminal of the electrometer during the constant voltage portion of the measurement
cycle.
The uncertainty of (𝑿 − 𝑿𝟎 ) is evaluated by a type A method using the results of repeated
measurements.
The uncertainty of
∆𝑽𝑿
∆𝒕𝑺
is comprised of the uncertainty of the voltmeter readings (range, non-
linearity, repeatability) and the uncertainty of the sampling time (accuracy, delay).
The uncertainty of 𝑪 is comprised of the uncertainty of the measured value of the capacitor at
1 kHz, the uncertainty of the 1 kHz to DC correction, and the effects of connection capacitance,
short term drift and temperature.
The uncertainties in 𝑰𝑷 , 𝑰𝑳 , 𝑰′𝑷 and 𝑰′𝑳 are estimated from the leakage resistances in the
measurement set-up and are considered insignificant for currents greater than 1 pA.
83
Nominal Current
: 95 pA
Quantity
Expected
Value
xi
Standard
Uncertainty
u(xi)
Distribution
Function
Sensitivity
Coefficient
ci
Uncertainty
contribution
u(yi)
Degree of
freedom
i
(𝑿 − 𝑿𝟎 )
-95.22 pA
0.005 pA
Normal
-0.0105 pA-1
-0.000053
7
0.095 17 V/s
0.000 008 V/s
Normal
-10.5 s/V
-0.000084
∞
0.000 00 V/s
0.000 008 V/s
Normal
+10.5 s/V
0.000084
∞
𝑪
1000.08 pF
0.05 pF
Normal
-0.001 pF-1
-0.000050
∞
𝑰𝑷, 𝑰𝑳 , 𝑰′𝑷 , 𝑰′𝑳
0 fA
∆𝑽𝑿
∆𝒕𝑺
∆𝑽𝟎
∆𝒕𝑺
Insignificant
Combined Uncertainty
Calibration
Factor
1.000 44
Nominal Current
0.000139
Expanded Uncertainty (95%)
0.00028
eff = 334
: 9.5 fA
Quantity
Expected
Value
xi
Standard
Uncertainty
u(xi)
Distribution
Function
Sensitivity
Coefficient
ci
Uncertainty
contribution
u(yi)
Degree of
freedom
i
(𝑿 − 𝑿𝟎 )
-9.516 fA
0.028 fA
Normal
-0.105 pA-1
0.002 8
11
0.951 4 V/s
0.000 08 V/s
Normal
1.05 s/V
0.000 08
∞
0.00 V/s
0.000 08 V/s
Normal
-1.05 s/V
-0.000 08
∞
𝑪
10.00 fF
0.05 fF
Normal
-0.1 fF-1
𝑰𝑷 + 𝑰𝑳 ,
0 pA
0.000 1 pA
Uniform
-105 pA-1
-0.011
∞
𝑰′𝑷 + 𝑰′𝑳
0 pA
0.000 1 pA
Uniform
105 pA-1
0.011
∞
∆𝑽𝑿
∆𝒕𝑺
∆𝑽𝟎
∆𝒕𝑺
Combined Uncertainty
Calibration
Factor
1.002 3
Expanded Uncertainty (95%)
-0.005
∞
0.016 6
0.033
eff > 104
84
Uncertainty Budget of METAS
It is required to report the value and uncertainty of
Q=
I
Iapplied
=
I
CS ∙
dV
dt
where I is the output of the UUT. From the expression above, the uncertainty on Q is:
𝑢
2 (𝑄)
2 𝑑𝑉
𝑢2 (𝐼) 𝑢 ( 𝑑𝑡 ) 𝑢2 (𝐶𝑆 )
=𝑄 [ 2 +
+
]
𝑑𝑉
𝐼
𝐶𝑆2
( )2
𝑑𝑡
2
The individual elements of the uncertainty on Q are:
Contribution of the UUT:
A measurement corresponds typically to 20 repetitions of a halt/ramp-up/halt/ramp-down cycle. We
build a measurement result by combining the 20 results of the cycles. Variability within a cycle is
tagged as noise. Variability between cycles characterizes short term stability. Uncertainty on I was
chosen as the maximum value between the short term stability and the noise uncertainties.
Contribution of the ramp generator:
𝑢2 (
𝑑𝑉
𝑑𝑉
1 2 1 𝐿𝑆𝐷𝑖𝑔𝑖𝑡 2
) = 𝑠2 ( ) + [ ] ∙ ∙ [
]
𝑑𝑡
𝑑𝑡
∆𝑡
3
2
where LSDigit/2 is the resolution of the voltmeter. We have noted that (𝑑𝑉/𝑑𝑡) shows a very
repeatable ripple that dominates the noise-like features. To simplify the analysis, we decided to treat
this ripple as a noise, which gives a pessimistic estimation of the uncertainty on the slope.
Contribution of the standard capacitor:
2
2
(𝐶𝑠 ) + [𝑡𝑒𝑚𝑝𝑐𝑜(𝐶𝑠 ) ∙ 𝑢(𝑇)]2 + 𝑢𝑓𝑟𝑒𝑞
(𝐶𝑠 )
𝑢2 (𝐶𝑠 ) = 𝑢𝑐𝑎𝑙𝑖𝑏
where 𝑢𝑐𝑎𝑙𝑖𝑏 is the uncertainty on the capacitance standard value determined at calibration. The
temperature coefficient 𝑡𝑒𝑚𝑝𝑐𝑜𝐶𝑠 is specified by the manufacturer. The temperature uncertainty is
0.5°C. Finally, 𝑢𝑓𝑟𝑒𝑞 is the uncertainty due to extrapolation to DC of capacitance values obtained in
AC.
Neglected:

Variation of the time interval between samplings of the voltmeter (stability better than 0.1
ppm in the measurement period).  Last significant digit truncation of the UUT (noise level
is much higher).
85





Burden voltage of UUT (has no influence at steady state).
Temperature, humidity and pressure coefficients of the UUT: it is assumed that the pilot
laboratory will use data from the participants to correct for the ambient conditions drift of
the UUT.
The effect of parasitic conductance of CS because of the symmetry of the measured
points.
Offset short term stability of the DVM because of the high repeatability observed in the
measurement of the slope.
Uncertainty on the DVM gain.
Uncertainty budget detailed calculations
Model function :
𝑄=
𝐼
∆𝑉
(𝐶𝑆_𝐶𝑎𝑙 ∙ 𝐾1 ∙ 𝐾2) ∙ (( ∆𝑡 ) ∙ 𝐾3)
Quantity
Definition
I
Unit under test (UUT) output
CS_cal
CS value from calibration
K1
Uncertainty factor on CS due to temperature
K2
Uncertainty factor on CS due to extrapolation to DC
V/t
Voltage ramp slope
K3
Uncertainty factor due to DVM resolution
Q
Result
Nominal Current : 95 pA
Expected
Value
Standard
Uncertainty
Sensitivity
Coefficient
Uncertainty
contribution
Degree of
freedom
xi
u(xi)
ci
u(yi)= ci· u(xi)

I
9.50496E-11
8.33E-16
Normal
1.05E+10
8.77E-06
19
CS_cal
1.00E-09
3.70E-15
Rectangular
1.00E+09
3.70E-06
∞
K1
1.00E+00
2.00E-15
Rectangular
1.00E+09
2.00E-06
∞
K2
1.00E+00
5.00E-06
Rectangular
1.00E+00
5.00E-06
∞
V/t
9.50041E-02
1.69E-06
Normal
1.05E+01
1.78E-05
19
K3
1.00E+00
1.67E-07
Rectangular
1.05E+01
1.75E-06
∞
Q
1.000446
Quantity
Distribution
Function
Combined Uncertainty
2.09E-05
Expanded Uncertainty (%95.5)
4.19E-05
35
86
Nominal Current : 9.5 fA
Expected
Value
Standard
Uncertainty
Sensitivity
Coefficient
Uncertainty
contribution
Degree of
freedom
xi
u(xi)
ci
u(yi)= ci· u(xi)

I
9.51957E-15
2.09E-17
Normal
1.05E+14
2.20E-03
19
CS_cal
1.00E-12
5.04E-18
Rectangular
1.00E+12
5.04E-06
∞
K1
1.00E+00
5.00E-21
Rectangular
1.00E+12
5.00E-09
∞
K2
1.00E+00
2.00E-05
Rectangular
1.00E+00
2.00E-05
∞
V/t
9.50038E-03
1.48E-06
Normal
1.05E+02
1.56E-04
19
K3
1.00E+00
1.67E-07
Rectangular
1.05E+02
1.75E-05
∞
Q
1.002019
Quantity
Distribution
Function
Combined Uncertainty
2.20E-03
Expanded Uncertainty (%95.5)
4.41E-03
19
87
Uncertainty Budget of HU-BFKH
Model Function: PAM2012 1100 pF capacitor
Nominal Current: -100, -50, 0, 50, 100 pA
Expected Value
Quantity
xi
Standard
Uncertainty Distribution
Function
u(xi)
Sensitivity
Coefficient
Uncertainty
contribution
Degree of
freedom
ci
u(yi)= ci·u(xi)
10-6
i
0
25·10-6
Gaussian
1
25
50
Triboelectric effect
of BNC
0 pA
0.0001 pA
Rectangular
1
1
∞
Input bias current
-0.007 pA
0.0005 pA
Rectangular
1
5
∞
Cable leakage
0 pA
0.0005 pA
Rectangular
1
5
∞
Normal resistor
1GΩ
1.00007761 GΩ
17 kΩ
Gaussian
1
17
∞
100 mV Source
Fluke5700
100.007761 mV
0.0012
Gaussian
1
12
∞
0 mV
0.003 mV
Rectangular
1
30
∞
Fitting deviations
Uncorrected offset
voltage
Combined Uncertainty
33.3
eff =157
Calibration factor
Expanded Uncertainty (%95.5)
67
88
Nominal Current : 95 pA
Expected
Value
Standard
Uncertainty
xi
u(xi)
Calibration of
PAM2012
1100 pF range
0
33·10-6
Reading noise
PAM
0
Reading noise
Keithley6430
Triboelectric
effect of BNC
Quantity
Input Bias
current
Cable leakage
Distribution
Function
Sensitivity
Coefficient
Uncertainty
contribution
Degree of
freedom
ci
u(yi)= ci·u(xi)
10-6
i
Gaussian
1
33
157
0.183 fA
Gaussian
1
1.93
10
0
0.0051 fA
Gaussian
1
0.05
1700
0
0.2 fA
Rectangular
1
2.11
∞
-0.007
0.5 fA
Rectangular
1
5.26
∞
0
0.1 fA
Rectangular
1
1.05
∞
Combined Uncertainty
33.6
Expanded Uncertainty (%95.5)
67
eff =168
Calibration factor
89
Uncertainty Budget of RISE
Model function
:
𝑄=
𝐼𝑡𝑠
𝐶
𝑑𝑉
𝑑𝑇
Nominal Current: 95 pA
Quantity
Capacitance
C
Voltage slope
dV/dt
Noise (Allan
deviation)
Calibration
Factor
Standard
Uncertainty
u(xi)
10-6
Distribution
Function
Sensitivity
Coefficient
ci
1 nF
21
Normal
1
21
2.4
95 mV/s
0.9
Rectangular
1
0.9
100
0
15
Normal
1
15
10
Capacitance
C
Voltage slope
dV/dt
Noise (Allan
deviation)
Calibration
Factor
u(yi)= ci·u(xi)
10-6
Combined Uncertainty
26
Expanded Uncertainty (%95.5)
69
Degree of
freedom
i
eff = 5
1
Nominal Current
Quantity
Uncertainty
contribution
Expected
Value
xi
: 9.5 fA
Expected
Value
xi
Standard
Uncertainty
u(xi)
10-6
Distribution
Function
Sensitivity
Coefficient
ci
Uncertainty
contribution
u(yi)
10-6
Degree of
freedom
i
10 pF
38
Normal
1
38
2.2
0.95 mV/s
2.5
Rectangular
1
2.5
100
0
3500
Normal
1
3500
10
Combined Uncertainty
3500
eff = 10
1
Expanded Uncertainty (%95.5)
8000
90
Uncertainty Budget of IPQ
Model function:
𝑄=
𝐼 + 𝑘𝐼
𝑑𝑉 + 𝑘𝑉
𝐶∙
𝑑𝑡
I
: Representing the readout of the instrument
kI
: A constant value of 0 associated to its limited resolution
C
: The value of the standard capacitor used for the current source
dV
: The voltage step to charge the capacitor
kV
: A constant value of 0 associated to its limited resolution
dt
: The charging time
For each of those final entry lines an uncertainty budget is presented, corresponding to the worst
standard uncertainty case found and belonging to the set of measurements that contribute to the
presented averaged Q. The calculation of the uncertainty was made in accordance with GUM –
“Guide to the Expression of Uncertainty in Measurement“. Through the previously referred model,
the related contributive uncertainties are due to the:
u(I)
: Standard deviation of the mean readouts (A)
u(kI)
: Limited resolution (A)
u(C)
: Calibration of the capacitors in use (F);
u(dV) : Characterization of voltage ramp (V)
u(kV) : Limited resolution (V)
u(dt) : Knowledge of trigger periods (s)
The resultant sensitivity coefficients have been applied:
𝜕𝑄
𝑑𝑡
=
𝜕𝐼 𝐶 ∙ (𝑑𝑉 + 𝑘𝑉 )
91
𝜕𝑄
𝑑𝑡
=
𝜕𝑘𝐼 𝐶 ∙ (𝑑𝑉 + 𝑘𝑉 )
𝜕𝑄
𝑑𝑡 ∙ (𝐼 + 𝑘𝐼 )
=− 2
𝜕𝐶
𝐶 ∙ (𝑑𝑉 + 𝑘𝑉 )
𝜕𝑄
𝑑𝑡 ∙ (𝐼 + 𝑘𝐼 )
=−
𝜕𝑑𝑉
𝐶 ∙ (𝑑𝑉 + 𝑘𝑉 )2
𝜕𝑄
𝑑𝑡 ∙ (𝐼 + 𝑘𝐼 )
=−
𝜕𝑘𝑉
𝐶 ∙ (𝑑𝑉 + 𝑘𝑉 )2
𝜕𝑄
𝐼 + 𝑘𝐼
=
𝜕𝑑𝑡 𝐶 ∙ (𝑑𝑉 + 𝑘𝑉 )
Nominal Current : 95 pA
Quantity
Expected
Value
xi
Standard
Uncertainty
u(xi)
Distribution
Function
Sensitivity
Coefficient
ci
Uncertainty
contribution
u(yi)= ci·u(xi)
Degree of
freedom
i
I
9.27E-11 A
2.71E-13 A
Normal
1.08E+10
2.92E-03
9
𝒌𝑰
0.00E+00 A
2.89E-16 A
Rectangular
1.08E+10
3.11E-06
50
C
1.00E-10 F
1.00E-15 F
Normal
9.99E+09
9.99E-06
50
dV
7.42E+00 V
6.03E-05 V
Rectangular
1.35E-01
8.12E-06
4
𝒌𝑽
0.00E+00 V
2.89E-07 V
Rectangular
1.35E-01
3.89E-08
50
dt
8.0 s
1.00E-12 s
Rectangular
1.25E-01
1.25E-13
50
Calibration
Factor
Combined Uncertainty
2.92E-03
eff = 9
1.0012
Expanded Uncertainty (%95.5)
6.8E-03
92
Nominal Current: 9.5 fA
Quantity
Expected
Value
xi
Standard
Uncertainty
u(xi)
Distribution
Function
Sensitivity
Coefficient
ci
Uncertainty
contribution
u(yi)= ci·u(xi)
Degree of
freedom
i
I
9.48E-15 A
8.34E-16 A
Normal
1.05E+14
8.73E-02
108
𝒌𝑰
0.00E+00 A
2.89E-18 A
Rectangular
1.05E+14
3.02E-04
50
C
1.00E-12 F
1.00E-17 F
Normal
9.93E+11
9.93E-06
50
dV
1.53E+00 V
3.01E-05 V
Rectangular
6.50E-01
1.96E-05
80
𝒌𝑽
0.00E+00 V
2.89E-07 V
Rectangular
6.50E-01
1.88E-07
50
dt
160.0 s
1.00E-12 s
Rectangular
6.20E-03
6.20E-15
50
Calibration
Factor
1.0012
Combined Uncertainty
8.73E-02
eff = 108
Expanded Uncertainty (%95.5)
1.8E-01
93
Appendix C: Technical Protocol
TECHNICAL PROTOCOL
EURAMET Supplementary Comparison
Comparison for Ultra-low DC Current Sources
Project 1381
TÜBİTAK UME
(Rev. 2)
February 08, 2019
Technical Protocol of the Comparison for Ultra-low DC Current Sources – EURAMET PROJECT 1381
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Contents
1.
Introduction .................................................................................................................................3
2.
Travelling Standard.....................................................................................................................3
3.
Organization ...............................................................................................................................4
4.
Participant Laboratories ..............................................................................................................4
5.
Time Schedule ............................................................................................................................5
6.
Transport Case ...........................................................................................................................6
7.
Transportation of Travelling Standard .........................................................................................8
7.1.
Failure of Travelling Standard ....................................................................................... 8
7.2.
Financial Aspects ........................................................................................................... 8
8.
Measurement Quantities and Points ...........................................................................................9
9.
Measurement Instructions .........................................................................................................10
10. Measurement Uncertainty .........................................................................................................10
11. Reporting of Results .................................................................................................................11
12. Final Report of the Comparison ................................................................................................12
13. References ...............................................................................................................................12
ANNEX 1 .........................................................................................................................................13
ANNEX 2 .........................................................................................................................................15
ANNEX 3 - The Receipt Form..........................................................................................................18
ANNEX 4 - The Dispatch Form ........................................................................................................19
ANNEX 5 – Measurement Report Form ...........................................................................................21
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1. Introduction
Supplementary comparison on this subject, EURAMET.EM-S24, was carried out from 2005 to
2009. The objective of this comparison is to provide technical evidence supporting their CMCs
entries of those participants who did not participate in the EURAMET.EM-S24, while other
participants would have an evidence for confirmation of their improvements in this field of
measurement. The comparison will be performed at the points of ± 9.5 fA, ± 95 fA, ± 0.95 pA, ±
9.5 pA, ± 95 pA. A commercial electrometer Keithley 6430 will be used as travelling standard.
TÜBİTAK UME is acting as the pilot laboratory. The travelling standard will be provided by
TÜBİTAK UME. TÜBİTAK UME will be responsible to monitoring standard performance during
the circulation and the evaluation and reporting of the comparison results.
The comparison will be carried out in accordance with the CCEM Guidelines for Planning,
Organizing, Conducting and Reporting Key, Supplementary and Pilot Comparisons [1].
2. Travelling Standard
There is one electrometer as travelling standard (Figure 1). The identifications are as follows:
Travelling Standard
Name
: Sub-Femtoamp Remote Source - Meter
Manufacturer
: Keithley
Model
: 6430
Serial No
: 4081508
Figure 1. Photos of travelling standards
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The travelling standard has very special input connectors, therefore it will be accompanied by
appropriate adapters with appropriate BNC connectors.
The travelling standard will be supplied by TÜBİTAK UME. The standard was chosen for its high
accuracy and stability in time.
Table 1. Details of the travelling standard
Device
Brand
Type
Serial
Number
Remarks
The instrument will be
Sub-femtoamp
Remote Source Meter
accompanied by
Keithley
6430
4081508
appropriate adapters and
cables.
3. Organization
Following the Guidelines for EURAMET key comparisons two institutes from the provisional list of
participants were nominated to help the pilot laboratory with the organization. These are SP
(T. Bergsten) and NSAI NML (O. Power). In the following the pilot laboratory and the helping
laboratories will be denominated as “the support group”. The TC chairman of the EURAMET EM
Working Group will be regularly informed about the progress of this comparison.
4. Participant Laboratories
The pilot institute for this comparison is TÜBİTAK UME (TURKEY). The contact details of the
coordinator are given below:
Pilot Laboratory :
TÜBİTAK UME
Coordinator
Enis TURHAN
:
Impedance Laboratory
TUBİTAK UME
Tel: +90 262 679 50 00
Fax: +90 262 679 50 01
E-mail: enis.turhan@tubitak.gov.tr
The participating institutes and contact persons with their shipping addresses are given in
Annex1.
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5. Time Schedule
The time schedule for the comparison is given in the Table 3. The circulation of travelling
standard will be organized so that to monitor the performance of the travelling standard. Each
laboratory will have 3 weeks to carry out the measurements and 2 weeks for transportation. Any
deviation in the agreed plan should be approved by the pilot institute.
The comparison will be organized in two loops of three laboratories in order to allow close
monitoring of the behavior of the standard. The pilot laboratory will measure the travelling
standards between two loops.
Table 3. Circulation Time Schedule
Acronym of
Institute
Country
Starting Date
Time for measurement
and transportation
TUBITAK UME
TURKEY
05.03.2018
4 weeks
LNE
FRANCE
26.03.2018
5 weeks
NSAI
IRELAND
30.04.2018
5 weeks
IPQ
PORTUGAL
04.06.2018
5 weeks
TUBITAK UME
TURKEY
09.07.2018
5 weeks
METAS
SWITZERLAND
03.09.2018
5 weeks
BFKH
HUNGARY
08.10.2018
5 weeks
SP
SWEDEN
12.11.2018
5 weeks
TUBITAK UME
TURKEY
17.12.2018
8 weeks
VNIIFTRI
RUSSIA
11.02.2019
8 weeks
TUBITAK UME
TURKEY
08.04.2019
5 weeks
In agreeing with the proposed circulation time schedule, each participating laboratory confirms
that it is capable to perform the measurements in the limited time period allocated in the time
schedule.
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If, for some reasons, the measurement facility is not ready or custom clearance should take too
much time, the laboratory has to contact immediately the co-ordinator in the pilot laboratory.
According to the arrangement made in this special case the travelling standards may be sent
directly to the next participant before the measurements have been finished or even without
performing any measurements. In such a case there will still be possibility for carrying out
measurements once again at the end of the comparison.
If delay occurs the pilot laboratory will inform the participants and revise - if necessary - the time
schedule, or skip one country and put it at the end of the circulation.
6. Transport Case
The standards have to be protected against excessive mechanical shocks. The travelling
standards and their accessories will be sent to you in one transport case that is suitable for
shipment as freight. Unless the transport case is damaged, it will be requested to use the same
case for transport of the standards to the next participant.
The dimensions of the case for the travelling standard are 39 cm height, 60 cm depth, 50 cm
width: the approximate weight being 16 kg (standard and accessories included).
The transport case contains the following items:

Keithley 6430 Source Meter S/N 4081508 without power cable

Keithley 6430 Remote Preamplifier with cable

Adapter
: GPIB-USB S/N 15B2F42

Adapter
: 3-Lug Triax(m) - BNC(f) (Guard removed)

Cable
: 3-Lug Triax(m)-BNC(m) ( 70 cm)

Cable
: BNC(m) – BNC(m) (30 cm)

Technical Protocol of Comparison
The pictures of adapters and cables sent with the device are shown in Table 4 for reference. In
the measurements both Triax(m)-BNC(m) cable or BNC(m)-BNC(m) cable with combination of
Triax(m)-BNC(f) adapter can be used.
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Table 4. Pictures of cables and adapters in transport case
Adapter
:
GPIB-USB S/N 15B2F42
Adapter
:
3-Lug Triax(m) - BNC(f)
(Guard removed)
Cable :
3-Lug Triax(m) - BNC(m) ( 70 cm)
Cable :
BNC(m) – BNC(m) (30 cm)
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7. Transportation of Travelling Standard
TUBITAK UME is responsible for the organization of transportation of the travelling standard.
The transportation of the standards to the next participant is on each participant’s responsibility.
The transportation may be arranged preferably hand carried by car or by a shipping agent,
courier or parcel delivery service of your choice. The transport case can easily be opened for
customs inspection.
The shipment should be arranged in a way that the time for transport is as short as possible. This
means that customs procedures, where appropriate, have to be examined in advance of the
transport. Particular care should be taken to avoid the shipping case being exposed to extreme
temperatures, e.g. left standing on the airport.
Upon arrival, the transport cases and their contents must be checked for visible damage. In case
the case or the standards are damaged, this should be reported to the person who delivers the
package. If you notice any damage, it is recommended to take pictures of it.
After arrival of the package, the pilot laboratory has to be informed of this by completing and
returning the receipt form (Annex A3) by e-mail.
The travelling instrument will be accompanied by an ATA carnet to accelerate customs
procedures. The value of the package is about 25.000 €.
Immediately after having completed the measurements, the package is to be transported to the
next participant. It is advisable to prepare and organize this transportation beforehand. Please,
inform the pilot laboratory again about the details of sending the package to the next participant
using the dispatch form (Annex A4) - and also inform the next participant by e-mail.
7.1. Failure of Travelling Standard
In case of any damage or malfunction of the travelling standard, the pilot laboratory must be
informed immediately.
7.2. Financial Aspects
Each participant laboratory is responsible for its own costs for the measurements as well as any
damage that may occur within its country.
The overall costs for the organization of the comparison are covered by the pilot laboratory. The
pilot laboratory has no insurance for any loss or damage of the travelling standard.
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8. Measurement Quantities and Points
The measurements are carried out by calibrating the transfer instruments, i.e. by supplying a DC
current specified by the participant’s current source and recording the instruments reading. The
measurands are then the calibration factors of the transfer instruments, defined as the ratio of
reading of the transfer instrument and supplied current.
The nominal values of the eight measuring points are +10 fA, -10 fA , +100 fA, -100 fA, +1 pA, -1
pA, +10 pA, -10 pA, + 100 pA, and -100 pA. In order to take full advantage of the transfer
instruments’ resolution and to avoid internal range switching the calibration points must be slightly
below the nominal values. Therefore, the calibration points should be 0.95 times the nominal
values, e. g. 95 fA, 0.95 pA, Only if for some technical reasons this might be impossible, the
exact nominal values may be used.
The quantities to be measured are given in Table 5.
Table 5. Measurement quantity & points
Quantity
Nominal Value
Current Measurement
Range
+9.5 fA
-9.5 fA
+95 fA
1 pA
-95 fA
+0.95 pA
DC Current
-0.95 pA
+9.5 pA
10 pA
-9.5 pA
+95 pA
100 pA
-95 pA
The main parameter is DC current. In addition, the quantities given below must be measured and
recorded;
 Ambient temperature
 Ambient humidity
 Atmospheric pressure
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The participants are not obliged to measure all of the values. The participant can choose the
measurement values in accordance with to the measurement capability.
No correction will be applied for the ambient temperature, relative humidity and atmospheric
pressure.
9. Measurement Instructions
Before the measurements, the travelling standard must be turned on and waited for the
stabilization for one day in the laboratory.
Instrument can and should be operated remotely. A GPIB-USB adapter will be provided with the
instrument. The instruction manual will not be supplied with the device. User manual of the device
is open source reachable from below link of manufacturer website:
https://www.tek.com/low-level-sensitive-and-specialty-instruments/high-resistance-low-currentelectrometers-series-650-0
After transportation a minimum settling and warm-up time of one day should be allowed for the
instrument. The measurements should be carried out at a temperature of (23 ± 1) °C and at a
relative humidity of (45 ± 15) %rh.
The transfer instrument has considerable time constants. To take this into account, a settling time
of 15-20 s after each current change must be allowed. Instructions specific commands for the
instrument are given in the Annex 2.
10.
Measurement Uncertainty
The uncertainty of measurement must be calculated according to the JCGM 100 “Guide to the
Expression of Uncertainty in Measurement” [2] for the coverage probability of approximately 95%.
All contributions to the measurement uncertainty should be listed in the report submitted by each
participant. A model equation with all relevant quantities must be supplied. The evaluation of
each uncertainty component has to be detailed.
Each laboratory should declare measurement uncertainty budget where they take into account
their measurement system uncertainty contributions, according to the format given Annex 5.
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11. Reporting of Results
The individual results with date, temperature, air pressure, humidity, measurement current,
measuring range of the instrument, readout, calibration factor, standard uncertainty, and degrees
of freedom will be reported to the pilot laboratory (please use the attached Measurement Report
form, Annex 5). For each nominal value a separate summary of results form has to be used.
For each nominal value, the result (which may have been obtained by combining several
measurements) has to be reported using one single line of sheet (item 6 in Annex 5). Only if a
participant observes that for a nominal value the scatter of several independent measurements is
incompatible with the uncertainty stated (maybe e.g. caused by drift or jumps of the transfer
standard) then he should document this fact by using several lines in the summary of results
sheet.
For each line used in the summary of results forms a detailed evaluation of the uncertainty of
measurement is required.
Furthermore, a short description of the measuring set-up used and the raw data are to be
reported. The raw data should be supplied as an excel-file. The source of traceability has to be
stated, since this may be a potential source of correlation. The report and the summary should
preferably be sent by e-mail.
The reports should be sent to the pilot laboratory no later than six weeks after the measurements
have been completed at the participant laboratory.
No information about differences of the reported results with respect to others will be
communicated before the completion of the comparison, unless very suspicious larger deviations
of particular laboratories results and the preliminary reference results obtained by the pilot
laboratory have been observed. In this case the laboratory in question will be contacted.
Results shall be reported to the pilot laboratory. The report must contain at least:
 Details of participating laboratory,
 The date of the measurements,
 A detailed description of the measurement method and system used,
 The measurement standards used in the comparison measurements,
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 The environmental conditions during the measurements,
-
ambient temperature
-
relative humidity
-
ambient pressure
 Results of measurement; the measurement results shall be provided according to the
Annex 5 format.
 A statement of traceability,
 Model function of measurement with explanations of the symbols,
 Expanded measurement
uncertainty,
estimated for the coverage probability of
approximately 95%.
12. Final Report of the Comparison
The draft and final versions of the comparison report will be prepared by the pilot laboratory. The
support group will decide how the reference value should be determined from the reported data.
The draft A report will be distributed to the participants within 6 months after the last
measurement results have been reported. The draft A report is confidential to the participants and
the support group. Comments on the draft A report should be sent to the pilot laboratory within 2
month after distribution of this report. The comments will be taken into account in the draft B
report. The draft B report will be distributed within about 12 months after the measurements have
been completed. While the pilot laboratory prepares the draft B report, the support group will be
asked to check the calculations of the results. The participants and support group will be allowed
2 months to report their comment on the draft B report. The final report will then be completed
within about 1 month after receiving the comments on the draft B report.
13. References
[1] CCEM Guidelines for Planning, Organizing, Conducting and Reporting Key, Supplementary
and
Pilot
Comparisons,
2007
(available
on
the
BIPM
website:
http://www.bipm.org/utils/common/pdf/CC/CCEM/ccem_guidelines.pdf)
[2] Evaluation of measurement data - Guide to the Expression of Uncertainty in Measurement
(GUM), JCGM 100, First edition, September 2008 (available on the BIPM website:
http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf)
[3] ISO / IEC 17043 “Conformity assessment — General requirements for proficiency testing”,
International Standardization Organization”, 2010
Technical Protocol of the Comparison for Ultra-low DC Current Sources – EURAMET PROJECT 1381
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ANNEX 1
Table 2. Participant List
Country
Institute
FRANCE
Laboratoire National de
Métrologie et d'essais
HUNGARY
Budapest Főváros
Kormányhivatala
IRELAND
National Standards
Authority of Ireland
PORTUGAL
Instituto Português da
Qualidade
Acronym
Shipping Address
Contact Person
LNE
Laboratoire national de métrologie et d'essais 29
Avenue Roger Hennequin - 78197 Trappes cedex,
FRANCE
Daniela Istrate
Daniela.Istrate@lne.fr
Tel : +33 1 30 69 10 00
Fax : +33 1 30 69 12 34
Government Office of the Capital City Budapest
Metrological and Technical Supervisory Department,
Section of Electrical, Thermophysical and Optical
Measurements
37-39 Németvölgyi Street
Budapest, H 1124
HUNGARY
Tibor Németh
nemeth.tibor@bfkh.gov.hu
Tel.: +36 1 4585-897
Fax: +36 1 4585-823
NSAI NML
NSAI National Metrology Laboratory
Griffith Avenue Extension
Glasnevin
Dublin 11
IRELAND
Oliver Power
Oliver.Power@nsai.ie
Tel.: +353 1 808 2610
Fax: +353 1 808 2603
IPQ
IPQ – Instituto Português da Qualidade
Rua António Gião, 2
2829-513 Caparica
PORTUGAL
Luis Ribeiro
LRibeiro@ipq.pt
Tel.:+351 212948161
BFKH
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Country
RUSSIA
Institute
Russian Metrological
Institute of
Technical Physics and
Radio Engineering
SWEDEN
RISE Research Institutes of
Sweden
SWITZERLAND
Federal Institute of
Metrology METAS
TURKEY
TÜBİTAK
Ulusal Metroloji Enstitüsü
Acronym
Shipping Address
Contact Person
VNIIFTRI
141570, Russia, Moscow Region, Mendeleevo,
VNIIFTRI
Dr. Sergey Sherstobitov
lab-610@vniiftri.ru
Tel.:+7 495 526 6390 (#9049)
Fax: +7 495 526 6321
RISE
RISE Research Institutes of Sweden
Measurement Science and TechnologyBox 857,
SE-501 15 Borås,
SWEDEN
Tobias Bergsten
tobias.bergsten@ri.se
Tel.: +46 (0)10 516 5116
METAS
Federal Institute of Metrology METAS
Lindenweg 50, 3003 Bern-Wabern,
SWITZERLAND
David Corminboeuf
david.corminboeuf@metas.ch
Tel.: +41 58 387 06 42
Fax: +41 58 387 02 10
TÜBİTAK
UME
TÜBİTAK Ulusal Metroloji Enstitüsü (UME)
TÜBİTAK Gebze Yerleşkesi
Barış Mah. Dr. Zeki Acar Cad. No:1
41470 Gebze-Kocaeli, TURKEY
Enis TURHAN
enis.turhan@tubitak.gov.tr
Tel.: +90 262 679 50 00
Technical Protocol of the Comparison for Ultra-low DC Current Sources – EURAMET PROJECT 1381
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ANNEX 2
OPERATING INSTRUCTIONS FOR THE KEITHLEY 6430
The preamplifier is already connected to the instrument using the appropriate cable. The
preamplifier's input connector to be used for the calibration is marked as "IN/OUT HIGH". The
"SENSE" input is not used.
The instrument is designed as a source-meter. It is able to both source and measure
current/voltage at the same time. In our case, both source functions must be disabled and only
the current measurement function should be enabled. Don’t be confused by the fact that currents
flowing into the instrument are displayed as negative currents and currents flowing out of the
instrument are displayed as positive currents. This is due to its design as a source-meter: its point
of view is the source inside the instrument. Nevertheless, with respect to the comparison currents
flowing into the instrument are to be counted positive and currents flowing out of the instrument
are to be counted negative. Therefore, the displayed current values must be multiplied by a factor
of -1.
The instrument can be operated remotely via GPIB interface or via RS-232 serial interface with
the following parameters:
RS-232 parameters: 9600 Baud, 8 bits, no parity, 1 stop-bit
Many filter functions are available in the instrument. To avoid correlation effects please use only
the repeat filter which implements an arithmetic averaging algorithm which is equivalent to
extending the integration time. Below in Table 1, there is a recommendation table for filter
settings according to the measured currents. These values are defined after a long time data
manipulations (these settings are recommendations and participants may change these settings
according to their measurement system needs).
To assure that all participants get comparable results the following commands (below in boldface) must be sent to the instrument via GPIB or RS-232 interface.
Technical Protocol of the Comparison for Ultra-low DC Current Sources – EURAMET PROJECT 1381
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*CLS
:SYST:AZER:STAT ON
:SYST:RCM SING
:SYSTEM:LFR 50
:SENS:CURR:NPLC 10
! Enable Auto Zero
! Auto range change mode Single
! Line frequency 50 Hz
! Measurement rate, high accuracy
!*************************** Config Volt ***********************************
:SOUR:FUNC VOLT
:SOUR:VOLT:MODE FIXED
:SOUR:VOLT:RANG 10E-3
:SOUR:VOLT 0
!*************************** Conf ig Current *******************************
:SENS:FUNC "CURR"
:SENS:CURR:PROT 105E-3
:FORM:ELEM CURR
!*************************** Current Range *******************************
There are two ways to adjust the current range:
:SENS:CURR:RANGE 1E-12
!Change this for the higher currents: 1E-11 and 1E-10
Or
:SENS:CURR:RANG:AUTO ON
:SENS:CURR:RANG:AUTO:LLIM 1E-12
! Change this for the higher currents: 1E-11 and
1E-10
!*************************** Trigger System****************************************
:DISP:DIG MAX
! Maximum resolution
:TRIG:SOUR IMM
! Continuous Trig
:TRIG:COUN 1
:ARM:SOUR IMM
! Continuous Arm
:ARM:COUN 1
Technical Protocol of the Comparison for Ultra-low DC Current Sources – EURAMET PROJECT 1381
16/23
!*************************** Filter settings**********************************
:AVER:AUTO OFF
! Auto Filter OFF
:AVER:REP ON
! REPEAT Filter ON
:AVER:REP:COUN 5
! Look for filter settings table, Insert here number of your
! choice
:AVER OFF
! MOVING Filter OFF
:AVER:ADV OFF
! ADVANCED FILTER OFF
:MED OFF
! MEDIAN FILTER OFF
Table 1. Recommended filter settings according to the measured current value
Repeat Filter
Current Value
Count
Moving
Filter
Noise
Tolerance
Median
Rank
Count
I ≤ 0.1 pA
5
1
0.1
0
0.1 pA < I ≤10 pA
4
1
0.1
0
I > 10 pA
3
1
0.1
0
The data transfer to the computer is initiated by the command:
:READ?
The instrument will respond with a text string giving the measured current in ampere.
Technical Protocol of the Comparison for Ultra-low DC Current Sources – EURAMET PROJECT 1381
17/23
ANNEX 3 - The Receipt Form
COMPARISON FOR ULTRA-LOW DC CURRENT SOURCES
The received date of transport case
Was there any serious damage on the
transport case?
Yes
No
Yes
No
Transport Case
Keithley 6430 Device
Remote Preamp with Cable
Was the contents of the transport
case completed?
GPIB-USB Adapter
Tiax(m)-BNC(f) Adapter
Tiax(m)-BNC(m) Cable (70 cm)
BNC(m)-BNC(m) Cable (30 cm)
Technical Protocol
After inspection, the travelling
standard is in working condition?
Yes
No
Is there an unexpected deviation from
the nominal value of the travelling
standards?
Yes
No
Remarks
The transport case was received by:
Institute
Contact Person
E-mail Address
Telephone No
Please send the form to the coordinator of the comparison!
enis.turhan@tubitak.gov.tr
Technical Protocol of the Comparison for Ultra-low DC Current Sources – EURAMET PROJECT 1381
18/23
ANNEX 4 - The Dispatch Form
COMPARISON FOR ULTRA-LOW DC CURRENT SOURCES
PROJECT 1381
The dispatch date of transport case
After inspection, the travelling
standard is in working condition?
Yes
No
Is there an unexpected deviation
from the nominal value of the
travelling standards?
Yes
No
Yes
No
Transport Case
Keithley 6430 Device
Remote Preamp with Cable
Is the contents of the transport
case completed?
GPIB-USB Adapter
Triax(m)-BNC(f) Adapter
Triax(m)-BNC(m) Cable (70 cm)
BNC(m)-BNC(m) Cable (30 cm)
Technical Protocol
Courier Name :
Shipping way
(Courier, in hand etc.)
Tracking No
:
Airline
:
Flight No
:
Date
:
Shipping to
(Participant Name & Address)
Remarks
Technical Protocol of the Comparison for Ultra-low DC Current Sources – EURAMET PROJECT 1381
19/23
The transport case was dispatch by:
Institute
Contact Person
E-mail Address
Telephone No
Please send the form to the next participant and the coordinator of the comparison!
enis.turhan@tubitak.gov.tr
Technical Protocol of the Comparison for Ultra-low DC Current Sources – EURAMET PROJECT 1381
20/23
ANNEX 5 – Measurement Report Form
MEASUREMENT REPORT
1. PARTICIPANT INFORMATION
Laboratory Name
Contact Person Name
Telephone No
Fax No
E-mail
Adress
2. MEASUREMENT DATE
3. ENVIRONMENTAL CONDITION
Temperature
:
(
±
) C
Relative Humidity :
(
±
) %rh
Pressure
(
±
) mbar
:
4. REFERENCES USED IN MEASUREMENT
Instrument Name
Manufacturer
Type / Model
Serial No
Treceability
5. MEASUREMENT METHOD
Technical Protocol of the Comparison for Ultra-low DC Current Sources – EURAMET PROJECT 1381
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6.
MEASUREMENT RESULTS (one sheet per standard and nominal current)
Nominal Current:
Date of
measurement
Ambient
temperature
Uncertainty
of ambient
temperature
Ambient
pressure
Uncertainty
of ambient
pressure
Ambient
humidity
Uncertainty
of ambient
humidity
Technical Protocol of the Comparison for Ultra-low DC Current Sources – EURAMET PROJECT 1381
Supplied
Current
Transfer
instrument’s
measuring
range
22/23
Reading of
transfer
instrument
Ratio
(Measurement
result)
Standard
uncertainty of
measurement
(combined
type A and B)
Degrees
of
freedom
7.
UNCERTAINTY BUDGET
Model function
:
Nominal Current
:
Quantity
Expected
Value
xi
Standard
Uncertainty
u(xi)
Distribution
Function
Sensitivity
Coefficient
ci
Combined Uncertainty
Calibratio
n Factor
Expanded Uncertainty (%95.5)
Uncertainty
contribution
u(yi)
Degree of
freedom
i
Effective
degrees of
freedom
eff =
23