IEC 61788-22-3:2022

Superconductivity - Part 22-3: Superconducting strip photon detector - Dark count rate

IEC 61788-22-3:2022 is applicable to the measurement of the dark count rate (DCR, RD) of superconductor strip photon detectors (SSPDs). It specifies terms, definitions, symbols and the measurement method of DCR that depends on the bias current (Ib) and operating temperature (T).
NOTE The data of measurement results in Annex A are based on measurements of one institute only. The standard will be updated after the data of a complete round robin test are available.

Supraconductivité - Partie 22-3: Détecteur de photons à bande supraconductrice - Taux de comptage en obscurité

L'IEC 61788-22-3:2022 s'applique au mesurage du taux de comptage en obscurité (DCR, RD) des détecteurs de photons à bande supraconductrice (SSPD). Elle spécifie les termes, les définitions, les symboles, ainsi que la méthode de mesurage du DCR qui dépend du courant de polarisation (Ib) et de la température de fonctionnement (T).
NOTE Les données des résultats de mesure figurant à l’Annexe A sont fondées sur les mesures d'un seul établissement. La norme sera mise à jour lorsque les données d'un essai interlaboratoire complet seront disponibles

General Information

• Status: Published
• Publication Date: 18-Aug-2022
• ICS: 29.050 - Superconductivity and conducting materials
• Technical Committee: TC 90 - Superconductivity
• Drafting Committee: WG 14 - TC 90/WG 14
• Current Stage: PPUB - Publication issued
• Start Date: 26-Aug-2022
• Completion Date: 19-Aug-2022

Standards Content (Sample)

IEC 61788-22-3 ®
Edition 1.0 2022-08
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Superconductivity –
Part 22-3: Superconducting strip photon detector – Dark count rate

Supraconductivité –
Partie 22-3: Détecteur de photons à bande supraconductrice – Taux de
comptage en obscurité
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IEC 61788-22-3 ®
Edition 1.0 2022-08
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Superconductivity –
Part 22-3: Superconducting strip photon detector – Dark count rate

Supraconductivité –
Partie 22-3: Détecteur de photons à bande supraconductrice – Taux de

comptage en obscurité
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 29.050 ISBN 978-2-8322-4070-0

– 2 – IEC 61788-22-3:2022 © IEC 2022
CONTENTS
FOREWORD . 4
INTRODUCTION . 6
1 Scope . 8
2 Normative references . 8
3 Terms, definitions and abbreviated terms . 8
3.1 Terms and definitions . 8
3.2 Abbreviated terms . 10
4 Principle of the measurement method . 10
5 Apparatus . 11
5.1 Detector packaging . 11
5.2 Cryogenic system . 11
5.3 Measurement system . 13
6 Measurement procedure . 14
6.1 Measurement of temperature . 14
6.2 Measurement of switching current . 14
6.3 Measurement of R . 15
D
7 Standard uncertainty . 16
7.1 Type A uncertainty . 16
7.2 Type B uncertainty . 16
7.3 Uncertainty budget table . 17
7.4 Uncertainty requirement . 18
8 Test report . 18
8.1 Identification of device under test (DUT) . 18
8.2 Measurement conditions and results . 18
8.3 Miscellaneous optional report . 19
Annex A (informative) Results of the round robin test. 20
A.1 DUT packages . 20
A.2 Measurement conditions . 20
A.3 Measurement results . 21
Bibliography . 25

Figure 1 – Example of one dark count pulse in the pulse train in inset . 9
Figure 2 – Schematic curve of R as a function of normalized bias current . 11
D
Figure 3 – Schematic diagram of a typical DCR measurement system . 12
Figure 4 – Equivalent circuit of the DCR measurement . 13
Figure 5 – Typical current-voltage (I-U) curve of an SSPD . 15
Figure A.1 – Photograph of the DUT with an SSPD and a temperature sensor . 20
Figure A.2 – I-U curve and R curves . 22
D
Table 1 – Uncertainty budget table for R . 18
D
Table A.1 – Test data of DUT . 22
Table A.2 – Temperature sensitivity and bias current sensitivity above a normalized
bias current of 0,9 . 23

Table A.3 – u and u above a normalized bias current of 0,9 . 23
A B
Table A.4 – Budget table for R at a bias point of 5,25 µA (I /I = 0,955) . 23
D b sw
Table A.5 – DCR values measured at a bias point of 5,25 µA (I /I = 0,955) . 24
b sw
Table A.6 – Temperature measurement . 24

– 4 – IEC 61788-22-3:2022 © IEC 2022
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
SUPERCONDUCTIVITY –
Part 22-3: Superconducting strip photon detector – Dark count rate

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
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rights. IEC shall not be held responsible for identifying any or all such patent rights.
IEC 61788-22-3 has been prepared by IEC technical committee 90: Superconductivity. It is an
International Standard.
The text of this International Standard is based on the following documents:
Draft Report on voting
90/489/FDIS 90/491/RVD
Full information on the voting for its approval can be found in the report on voting indicated in
the above table.
The language used for the development of this International Standard is English.
This document was drafted in accordance with ISO/IEC Directives, Part 2, and developed in
accordance with ISO/IEC Directives, Part 1 and ISO/IEC Directives, IEC Supplement, available
at www.iec.ch/members_experts/refdocs. The main document types developed by IEC are
described in greater detail at www.iec.ch/standardsdev/publications.

A list of all parts in the IEC 61788 series, published under the general title Superconductivity,
can be found on the IEC website.
The committee has decided that the contents of this document will remain unchanged until the
stability date indicated on the IEC website under webstore.iec.ch in the data related to the
specific document. At this date, the document will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
IMPORTANT – The "colour inside" logo on the cover page of this document indicates that it
contains colours which are considered to be useful for the correct understanding of its
contents. Users should therefore print this document using a colour printer.

– 6 – IEC 61788-22-3:2022 © IEC 2022
INTRODUCTION
IEC 61788-22 (all parts) is a series of International Standards on superconductor electronic
devices. Superconductivity enables ultra-sensitive sensing or detection of a variety of
measurands. IEC 61788-22-1 [1] lists various types of superconductor sensors and detectors.
The strip type in this document is one of them.
A typical fundamental structure of strip type detectors is a meander superconductor line, for
example, with a thickness of less than 10 nm, a width of less than 100 nm or a few 100 nm, and
a length of a few mm. The structure is in the nanoscale. ISO TS 80004-2:2015 [2] defines the
nanoscale as a length range approximately from 1 nm to 100 nm. Because nano-objects have
one or two dimensions in the nanoscale, superconductor meander lines are categorized as a
nano-object.
The term "nanowire" is frequently used for superconductor meander lines, but it is not
recommended in this document. In the ISO vocabulary, a nanowire is defined as an electrically
conducting or semi-conducting nanofibre with two external dimensions in the nanoscale, with
the third dimension being significantly larger. The two external dimensions of the nanowires are
in the nanoscale range, approximately from 1 nm to 100 nm. When the first two dimensions
differ significantly, a "nanoplate," "nanoribbon," or "nanotape" shall be used for the meander
line shape. However, in the field of electronics, these terms are not common. In addition to the
ISO definition of nano-objects, the shape of the superconductor meander lines may not fit the
shape of common wires that have a round cross-section. Although there are cases in which a
superconductor line shape falls into the category of nanowire (e.g. a superconductor line with
a thickness of 10 nm and a width of 100 nm), the theoretical treatment of single photon detection
mechanisms still requires "strip" rather than "nanowire": the width is wider than coherence
length and thus the superconductor line has a two-dimensional nature. Therefore,
IEC 61788-22-1 assigns the word "strip" or "nanostrip" to the meander line shape. According to
the nomenclature of the standard, the strip type detector is called superconductor strip photon
detector (SSPD) or superconductor nanostrip photon detector (SNSPD). The abbreviated term
SSPD is used in this document.
SSPDs are usually cooled down to a temperature well below the critical temperature and
current-biased with a bias value close to, but smaller than, its switch current. The photon
detection mechanisms can be described by Cooper-pair breaking, leading to hotspot formation
or vortex motion, followed by electrothermal feedback creating a resistive region [3], [4].
Although an exact detection model has not been established yet, it is true that photon absorption
leads to Cooper pair breaking that creates quasiparticles because the photon energy in a
telecommunication wavelength band (~ 1 eV) is typically 2 to 3 orders of magnitude higher than
the binding energy of a Cooper pair (~ meV). The photon absorption may create a normal-
conducting local-hotspot in the nanostrip. With an electrothermal feedback process, the normal
conducting domain expands across the width of the nanostrip and along the current flow
direction, leading to a voltage drop in the superconductor nanostrip. Other possible models are
vortex-antivortex depairing, in which two vortices move toward the opposite strip edges, and
single vortex crossing. Such vortex motion also creates a voltage drop, which can be followed
by resistive domain creation with the same electrothermal feedback mechanism. Because of
the resistive domain in the strip, the bias current is diverted to a readout circuit. The normal
conducting region will be cooled down rapidly and finally disappear. The above process
produces a voltage pulse which corresponds to an event of single photon absorption.
Typical application areas of SSPDs include quantum information, laser communication, light
detection and ranging, fluorescence spectroscopy and quantum computing. The SSPDs
outperform such single photon detectors as photomultipliers and avalanche photodiodes in
performance measures listed in the next paragraph. Due to the increasing needs for ultra-
sensitive photon detection in a range of visible to mid-infrared wavelengths, the SSPD market
___________
Figures in square brackets refer to the Bibliography.

is growing quickly. The standardization of SSPDs is beneficial to not only the industrial
application, but also detector development.
For photon detection, there are fundamental parameters, such as detection efficiency, timing
jitter, dead time and dark count rate. The dark count rate affects the measurement of other
parameters. For this reason, priority is given to the dark count rate. This document
(IEC 61788-22-3) defines a measurement method of dark count rate (DCR).

– 8 – IEC 61788-22-3:2022 © IEC 2022
SUPERCONDUCTIVITY –
Part 22-3: Superconducting strip photon detector – Dark count rate

1 Scope
This part of IEC 61788 is applicable to the measurement of the dark count rate (DCR, R ) of
D
superconductor strip photon detectors (SSPDs). It specifies terms, definitions, symbols and the
measurement method of DCR that depends on the bias current (I ) and operating temperature
b
(T).
NOTE The data of measurement results in Annex A are based on measurements of one institute only. The standard
will be updated after the data of a complete round robin test are available.
2 Normative references
There are no normative references in this document.
3 Terms, definitions and abbreviated terms
3.1 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following
addresses:
• IEC Electropedia: available at http://www.electropedia.org/
• ISO Online browsing platform: available at http://www.iso.org/obp
3.1.1
dark count
count recorded without any incident photon
Note 1 to entry: An example of one dark count is shown in Figure 1. The inset of Figure 1 shows a pulse train of
many dark counts, which have the same pulse shape.

Figure 1 – Example of one dark count pulse in the pulse train in inset
3.1.2
dark count rate
DCR
R
D
number of dark counts per unit of time
Note 1 to entry: R is equal to the sum of R and R as defined below.
D Db Di
3.1.3
background dark count rate
R
Db
DCR originating from blackbody radiation of optical components and stray photons
3.1.4
intrinsic dark count rate
R
Di
DCR originating from spontaneous occurrence of resistance inside a superconductor strip
3.1.5
bias current
I
b
direct current flowing through a superconductor strip that forms an SSPD to hold operating
condition
3.1.6
switch current
I
sw
maximum bias current for photon counting operation
Note 1 to entry: The I value can be determined as the highest supercurrent on a static current-voltage (I-U) curve.
sw
Since a strip goes to normal conducting state locally by electrothermal feedback mechanism, the I value is usually
sw
lower than the critical current, at which the whole strip becomes the normal conducting state.

– 10 – IEC 61788-22-3:2022 © IEC 2022
3.1.7
normalized bias current
I /I
b sw
bias current divided by switch current
3.1.8
retrapping current
I
r
current at which an SSPD resumes a superconducting state from a normal conducting state
when the bias current is reduced from a high value above I
sw
3.2 Abbreviated terms
R dark count rate
D
R background dark count rate
Db
R intrinsic dark count rate
Di
I bias current
b
I switch current
sw
T temperature
t time interval
I retrapping current
r
V output pulse amplitude
pp
N number of measurements at a specific I and T
b
u type A standard uncertainty of R
A D
u type B standard uncertainty of R
B D
4 Principle of the measurement method
DCR is divided into two components: background DCR (R ) that originates from blackbody
Db
radiation of optical components and stray photons at any I value and intrinsic DCR (R ) that
b Di
originates from spontaneous occurrence of resistance inside superconductor strips and is
dominant in a high I region near I .
b sw
Figure 2 shows a schematic curve of the bias current dependence of R , which is called the R
D D
curve. In the measurement setup with an SSPD coupled to an optical fibre for signal input, the
R component is dominant in a low I region, while the R component is dominant in a high I
Db b Di b
region. The R component that has a relatively weak dependence on I and equals the product
Db b
of the detection efficiency and the sum of blackbody photons and stray photons. On the other
hand, the R component is related to the events of spontaneous voltage-drop occurrence
Di
probably due to vortex dynamics related to inherent properties of superconductor strips.
Since R strongly depends on user’s environment, R curves shall be measured in a high bias
Db D
current region of I /I (> 0,8 in Figure 2), in which R is dominant with a negligible contribution
b sw Di
of R .
Db
The R curves shall be measured by counting output pulses for a certain period at different I
D b
points while the temperature of the SSPD is held constant at an operating temperature
recommended by a manufacturer. There is an approximately linear relation between lg(R ) and
D
normalized bias current in I /I > 0,8, as shown in Figure 2.
b sw
R is dominant in the low bias region.
Db
R is dominant in the high bias region.
Di
Figure 2 – Schematic curve of R as a function of normalized bias current
D
5 Apparatus
5.1 Detector packaging
Before characterizing an SSPD, it is necessary to make a detector package. For applications,
the most important purpose of packaging is to effectively couple the light to the SSPD active
area. A high coupling efficiency ensures a high detection efficiency. However, for the
measurement of R of the SSPD, optical coupling is optional.
Di
When optical coupling is optionally installed, fibre optical coupling is one of the most common
methods. The optical fibre shall be fixed in the block with effective and stable light coupling to
the detector. The temperature of the fibre end shall be the same as the block to minimize R .
Db
The fibre core shall be axially aligned to the SSPD active area surface to ensure good optical
coupling.
For the measurement of R , the SSPD shall be fixed to the packaging block using conductive
Di
silver paste or low-temperature conducting epoxy to ensure good thermal contact. The SSPD
shall be surrounded by the block material so that no blackbody radiation causes a temperature
rise of the SSPD. The block should be made of oxygen-free copper and equipped with a radio
frequency (RF) connector.
5.2 Cryogenic system
The most commonly used cryogenic system for SSPD operation is a cryostat based on a closed-
cycle mechanical cryocooler, e.g., Gifford-McMahon (GM) cryocooler or a pulse-tube cryocooler,
which provides a base temperature of less than 4 K. The packaging block is mounted on a cold
head plate with good thermal contact to obtain the identical temperature as that of the plate. It
is noted that a geomagnetic field causes no observable change in DCR, so that a magnetic
shield is unnecessary.
The temperature of the packaging block shall be measured by a calibrated temperature sensor
during the R measurement. The procedure of the temperature measurement is provided in 6.1.
D
– 12 – IEC 61788-22-3:2022 © IEC 2022
The fibre and coaxial cables should be installed inside the cryostat to provide the optical and
electronic connection between the detector package and the measurement circuit at room
temperature.
As shown in Figure 3, one end of the fibre (blue line) is fixed on the detector package. The
other end of the fibre is connected to a fibre connector (blue square) on the cryostat chamber
, the fibre should be removed, then
surface at room temperature. For the measurement of R
Di
the detector is fully shielded from blackbody radiation and stray photons.

Figure 3 – Schematic diagram of a typical DCR measurement system

Figure 4 – Equivalent circuit of the DCR measurement
5.3 Measurement system
The schematic diagram of a typical measurement system for the DCR measurement and the
equivalent circuit are shown in Figure 3 and Figure 4, respectively. The SSPD in the detector
package is connected to the bias tee through a coaxial cable. The voltage source in series with
the bias resistor (R ) supplies a stable bias current to the SSPD. The tolerance of the bias
b
resistor shall be better than ±0,01 % (the ± sign here means the upper and lower tolerance
limits, which is different from the expanded uncertainty). The bias current is fed to the detector
through the direct current (DC) port of the bias tee, and output pulses are extracted from the
RF port and then amplified by a wideband low noise RF amplifier. The amplifier shall cover
100 kHz to 500 MHz at least to avoid pulse waveform distortion. The amplifier input impedance
shall be 50 Ω to achieve a return loss over 15 dB to reduce back-reflected pulses. The amplified
pulses should be monitored by an oscilloscope, and shall be counted by a counting instrument.
A better signal-to-noise ratio can be obtained when a suitable bias tee and an amplifier are
operated at a low temperature. However, the cryogenic operation is optional, since no change
in DCR is expected by adjusting a threshold value for counting output pulses properly.
In order to reduce or eliminate environmental electromagnetic noise, all the electronics in the
measurement system are shielded by a metallic shell, which also should be connected to the
earth terminal. To avoid the potential difference among the circuit components, stabilize phase
voltage with reference to the earth and limit transient voltage; the resistance to the earth should
be less than 4 Ω. The length of the earth wire from the instruments to the earth should be less
than 2 m.
– 14 – IEC 61788-22-3:2022 © IEC 2022
6 Measurement procedure
6.1 Measurement of temperature
A cryogenic temperature sensor, e.g. Si diode, with a calibrated accuracy of ±12 mK in a working
temperature range shall be used to monitor T and its fluctuation of the detector package, which
shall be firmly attached to the package block or as close to the block as possible. The operating
temperature shall be kept constant by using a temperature controller with a heater attached to
the cold head.
Because DCR is sensitive to temperature, it is necessary to measure its fluctuation during the
DCR measurement. The fluctuation is defined as the highest and lowest temperatures
subtracted by an average temperature.
Typically, the short-term temperature fluctuation of the cryocooler cold head can be kept below
12 mK. However, long-term fluctuation can be influenced by the environmental temperature.
Therefore, during the DCR measurements, T values should be recorded periodically more than
ten times.
The average temperature value during the R measurement shall be reported as stated in
D
Clause 8. The required temperature regulation is ±0,5 % of an average temperature during
measurement. DCR measurements at different operating temperatures may be reported for a
wide range of applications.
6.2 Measurement of switching current
The switch current (I ) shall be measured before R measurement. The detector package shall
sw D
be cooled in a cryostat with a mechanical cooler or a liquid cryogen to a base temperature,
which shall be regulated. When the reading value of the temperature controller reaches the
operating temperature, an interval of more than 10 minutes should be required before starting
I-U curve measurement. The I-U curve measurement should be carried out using the DC
channel in Figure 3, where the voltage source is connected to R and the detector in series.
b
Figure 5 shows a typical I-U curve.
Two-terminal I-U measurement instead of four-terminal measurement may be used owing to
the high resistance of the SSPD in a normal conducting state. The procedure for the I-U curve
measurement should be as follows.
a) The voltage of a voltage source should be scanned up and down gradually so that a static
I-U curve is obtained.
b) The DC voltage drop across the SSPD (U ) should be measured by a voltmeter.
SSPD
a)
The current flowing in the detector can be calculated from U , R and U by using
source b SSPD
UU−
source SSPD
II . The scan loop reaches the highest current at I . Beyond this
SSPD R sw
b
R
b
point, the I decreases along the load line. After a part of the strip becomes normal
SSPD
conducting, U increases further. When the volage is reduced from the maximum
SSPD
voltage, the SSPD returns to a zero-voltage state at I .
r
==
Figure 5 – Typical current-voltage (I-U) curve of an SSPD
6.3 Measurement of R
D
The DCR measurement procedure shall be as follows.
a) The temperature of the detector package shall be set at a proper operating temperature
recommended for the use of the SSPD.
b) The temperature fluctuation during the DCR measurement shall be regulated within ±0,5 %
of an average temperature.
c) The discrimination voltage of the photon counting shall be set at a value between 0,5 V
pp
and 0,9 V , where V is the amplitude of the detector output pulses. The V is equal to
pp pp pp
50 Ω (I – I ) G, where G is the gain of the amplifier.
b r
d) The pulse counter records the number of dark counts generated in a time interval (t). The
time interval of the counter shall be set at a value, for example 10 s, so that the type A
relative standard uncertainty of u / R is less than 14 % that is given in 7.4. R is obtained
A D D
by dividing the count number by t.
e) R at each specific I point shall be recorded N times. Average values of R shall be
D b D
calculated using Formula (1). N shall be more than 10.
N
RR=
(1)
DD∑ j
N
j=1
f) An R curve shall be measured by increasing I at a certain small step in a range between
D b
0,9 × I and I so that the number of data points is more than 5. The procedure described
sw sw
in d) to e) shall be repeated until I reaches just below I .
b sw
g) The dependence of R curves on temperature may optionally be measured by changing the
D
operating temperature. The procedure described in d) to f) shall be repeated when the
temperature dependence is measured.

– 16 – IEC 61788-22-3:2022 © IEC 2022
7 Standard uncertainty
7.1 Type A uncertainty
The type A uncertainty of R , which is the measurement uncertainty based on statistical analysis,
D
is evaluated by measuring R N times at each normalized bias point I /I [5] [6].
D b sw
The standard uncertainty u that is the standard deviation of the average DCR shall be
A
calculated by Formula (2) at each I point.
b
N
u ()RR− (2)
A ∑ Dj D
N
j=1
The u value at a normalized bias current of 0,955, which is the second highest value in
A
Table A.3, is used for making the budget table of Table 1 and evaluating the standard
uncertainty of this measurement method. The normalized bias point 0,955 is suitable for this u
A
evaluation, since the R value at that bias point is large enough for statistical analysis and
D
moreover both sensitivities of R to temperature and current are calculable in 7.2 (Type B
D
uncertainty).
The maximum relative standard uncertainty of u / R shall be kept less than 14 % at any bias
A D
point, as required in 7.4.
7.2 Type B uncertainty
The type B uncertainty of R , which is the evaluation of uncertainty by methods other than
D
statistical analysis, includes uncertainty arising from fluctuation in the temperature
measurement and the voltage source for the current bias [5] [6]. The uniform probability density
function is assumed for calculating the standard deviation of temperature u and current u . The
T I
u is expressed by Formula (3),
B

∂∂R R

DD
(3)
u ×+uu ×

B  T
I
b
∂∂TI

b
where ∂∂RT/ is the sensitivity of R to a variation of temperature T, ∂∂RI/ is the
D D Db
sensitivity of R to a variation of bias current I ; u and u are the standard deviation values of
D b T Ib
temperature and current, respectively.
=
=
The ∂∂R / T and ∂∂R / I values are calculated at each point in a range of over I /I = 0,9
D Db b sw
for the data in Annex A, as an example. The temperature sensitivity is evaluated by using an
expression of [R (2,26 K) – R (2,34 K)] / 0,08 K, which is 195 098,8 cps/K at I /I = 0,955.
D D b sw
The current sensitivity expressed by [R (5,20 µA) – R (5,30 µA)] / 0,1 µA is 73 791,0 cps/µA at
D D
5,25 µA (I / I = 0,955) at an operating temperature of 2,300 K. Since ∂∂R / I at 5,30 µA is
b sw Db
unobtainable, the data at 5,25 µA are used to complete Table 1. Table A.2 shows that the
∂R ∂R

D D
relative sensitivity values of / R (≈ 30 % to 36 %) and / R (≈ 13 % to 14 %) are

 D D
∂T ∂I

b
almost independent of T and I , so that the relative type B uncertainty is also almost
b
independent of T and I . The calculation using the data at 5,25 µA is statistically more accurate
b
than those at lower bias points, since the R value is highest except one at 5,30 µA. Therefore,
D
the uncertainty calculation using the data at 5,25 A is acceptable.
The u value is evaluated by a standard deviation originating from the precision of the
T
temperature sensors and the random temperature fluctuations of the cryogenic system. A Si
diode temperature sensor has a calibrated accuracy of ±12 mK in a working temperature range
of 1,4 K to 10,0 K. It is assumed that temperature sensors have a uniform probability density
function of ±12 mK that means the upper and lower tolerance limits of temperature calibration.
The standard deviation of temperature sensor is 24 mK/2/ 3 ≈ 6,9 mK. The required
temperature regulation in 7.4 is ±0,5 % of an average temperature during measurement. At
2,3 K in the measurement of Annex A, it is ±11,5 mK and the standard deviation is
23 mK / 2 / 3 ≈ 6,6 mK. The measured random fluctuation of temperature in the
measurement of Annex A is around ±5 mK, which is well below the requirement. Therefore, the
standard deviation of temperature in this document is u (6,9 mK)+≈(6,6 mK) 9,5 mK .
T
The u value is evaluated by the standard deviation originating from the typical precision of
Ib
voltage sources and the tolerance of the bias resistor. The root mean square of noise of the
voltage source used in Annex A is 10 µV, so the standard deviation of 10 µV is maximum at
zero output voltage. At a higher output voltage, it becomes smaller. The maximum value is used
for the budget table. Taking the resistance of the standard bias resistor as 20 kΩ with a
tolerance of ±0,01 % (the ± sign here means the upper and lower tolerance limits, which is
3 ≈
different from the expanded uncertainty), the standard deviation is 20 kΩ × 0,000 1 /
1,15 Ω in a uniform probability density function. The variance of U/R at 0,106 V (I = 5,25 µA)
b b

U
2 2 2 -7 2
in Figure A.2 is u = (10 µV / 20 kΩ) + (0,106 V / (20 kΩ) × 1,15 Ω) ≈ 3,43 ×10 (µA) .

R
b
-4
Therefore, the u of 5,9 ×10 µA is used for the evaluation in 7.3.
Ib
7.3 Uncertainty budget table
The typical estimation of the standard uncertainty in this document is summarized in Table 1.
The total standard uncertainty value of u at a specific I value of 5,25 µA (I /I = 0,955) is
total b b sw
calculated by summing the type A uncertainty u and the type B uncertainty u according to the
A B
propagation law. The u value at 5,25 µA represents the total standard uncertainty of this
total
document as described in 7.1 and 7.2.
=
– 18 – IEC 61788-22-3:2022 © IEC 2022
Table 1 – Uncertainty budget table for R
D
Factor Parameter Symbol of Standard
Contribution to
symbol standard Sensitivity deviation of
u
deviation and coefficient parameter
total
type
N times
R u , A
− 148,1 cps 148,1 cps
D A
measurement
u , B
Temperature T 195 098,8 cps/K 9,5 mK 1 853,4 cps
T
−4
u , B
Current I 73 791,0 cps/µA 5,9 ×10 µA 43,5 cps
I
u
Combined standard uncertainty 1 859,8 cps
total
Relative standard uncertainty 34,4 %
R ± expanded uncertainty
D
5 414,0 ±3 719,6 cps
(coverage factor k = 2)
7.4 Uncertainty requirement
The temperature during the DCR measurement shall be regulated within the upper and lower
limits of ±0,5 % of an average temperature.
As shown in the uncertainty budget in Table A.1, the contribution to the total uncertainty u
total
is dominated by the temperature uncertainty. Therefore, in order not to significantly exceed the
level of the standard uncertainty in Table 1, the value of u , which is the standard deviation
A
value of the multiple measurement of R , at the highest bias current should be less than 5 × u
D A
in Table 1. Correspondingly, the relative standard uncertainty of u / R (= 5 × 148,1 / 5 414,0)
A D
shall be less than 14 %. When u / R at the highest bias current exceeds this value, the
A D
measurement apparatus shall be improved to meet this requirement.
8 Test report
8.1 Identification of device under test (DUT)
The DUT shall be identified as follows:
– name of the manufacturer of the DUT;
– DUT serial number or equivalent identification;
– superconductor material and substrate;
– structure of the SSPD;
– fibre coupling method.
8.2 Measurement conditions and results
The measurement conditions and results shall be recorded as follows:
– I value;
sw
– R curve(s) as a function of normalized bias current;
D
– relative standard uncertainty (u / R ) of R at the highest I point;
A D D b
– average temperature;
– standard deviation of temperatures during the R measurement;
D
– the fluctuation of the temperature of an average temperature during the R measurement
D
(the required temperature regulation is ±0,5 %).
8.3 Miscellaneous optional report
The following data may be reported optionally:
– R curve(s) as a function of normalized bias current at different operating temperatures;
D
– I-U curve at operating temperature;
– specification of the temperature sensor: model, temperature range, calibration accuracy;
– fibre connection structure inside the cryostat: connector, mechanical slice, or fusion slice;
– detector mount method in the cryostat
– method avoiding stray photons;
– configuration of the electric measurement system.

– 20 – IEC 61788-22-3:2022 © IEC 2022
Annex A
(informative)
Results of the round robin test
A.1 DUT packages
The SSPDs were fabricated in Shanghai and packaged in copper blocks. A temperature sensor
was rigidly mounted on the package, in order to avoid the inconsistency of the test results during
round robin tests. The DUT is shown in Figure A.1.

Figure A.1 – Photograph of the DUT with an SSPD and a temperature sensor
A.2 Measurement conditions
a) Temperature: the temperature was set at 2,300 K by using a temperature
...