Paper 3EC01 at ASC2010, to appear in IEEE Trans. Appl. Supercond. 21 (2011)
1
Investigation of Low-frequency Excess Flux
Noise in dc SQUIDs at mK Temperatures
Dietmar Drung, Jörn Beyer, Jan-Hendrik Storm, Margret Peters, and Thomas Schurig
Abstract—The excess low-frequency flux noise in dc superconducting quantum interference devices (SQUIDs) operated at
ultra-low temperatures was studied. A large number of single
SQUIDs as well as SQUID arrays from 16 wafers fabricated over
a period of six years were characterized at 4.2 K and <320 mK.
Considering the large spread in the low-frequency noise at 4.2 K,
there was no observable dependence of the low-frequency energy
resolution ε1/f on the SQUID design or fabrication parameters. In
contrast, below 4.2 K the low-frequency noise changed moderately or increased strongly depending on whether the bottom Nb
or the insulation layer were fabricated in our newer sputter
system instead of the older one. The corresponding excess noise
levels ε1/f at <320 mK and f = 10 Hz are typically 40 h and 300 h,
respectively (h is Planck’s constant). The excess noise scales as
ε1/f ∝ f -αα with α typically around 0.6 for good devices. For devices
with strong low-frequency excess noise, α increases up to about
0.9. The best energy resolution ε achieved so far with a 50 pH test
SQUID operated at 16 mK is 0.62 h at 100 kHz, increasing to
1.64 h at 1 kHz and 14 h at 10 Hz.
Index Terms—1/f flux noise, energy resolution, SQUID current
sensor, ultra-low temperature.
I. INTRODUCTION
T
he dc superconducting quantum interference device
(SQUID) is a highly sensitive detector of magnetic flux
[1]. Commonly, an input coil is magnetically coupled to the
SQUID loop thereby creating a low-noise current sensor. In
August 2003, the first PTB current sensor wafer was
fabricated. Since then, various current sensor design versions
C1 to C6 were developed [2]-[5], and over 1000 SQUIDs were
tested in liquid helium. Originally, most of our current sensors
were operated at T = 4.2 K. Since 2005, we deliver an increasing number of SQUIDs for applications where the device
is operated at mK temperatures, e.g., the readout of transitionedge sensors (TESs) [6] or metallic magnetic calorimeters
(MMCs) [7]. For these applications, the SQUIDs are carefully
selected by using the characterization at 4.2 K and considering
the typical trend in the SQUID parameters between 4.2 K and
<1 K. SQUID characterization at mK temperatures is done on
sample basis to check the fabrication quality, or in cases where
the user wishes devices 100% tested at the intended working
temperature. This way, we collected flux noise data at 10-320
mK for a variety of SQUIDs of different designs from wafers
fabricated over a period of six years.
Manuscript received 3 August 2010. This work was supported in part by
the European Commission in the framework of the European Microkelvin
Collaboration.
The authors are with the Physikalisch-Technische Bundesanstalt (PTB),
Abbestraße 2-12, D-10587 Berlin, Germany (phone: +49-30-3481-7342; fax:
+49-30-3481-69-7342; e-mail: dietmar.drung@ptb.de).
Low-frequency excess flux noise in SQUIDs (in particular
at ultra-low temperatures [8]) remained a challenge for over
20 years; recently, the interest in this topic increased [9]-[12].
For our SQUIDs, a degradation in the low-frequency noise
performance is observed when the devices are cooled to mK
temperatures, and the 1/f noise corner (the frequency for equal
1/f and white noise densities) moves from typically below
10 Hz at 4.2 K to above 1 kHz at mK temperatures. This is a
severe problem for MMC readout [7] and other applications
below about 10 kHz where SQUID noise limits the overall
signal-to-noise ratio. To address this issue, we measured a
series of SQUIDs both at 4.2 K and near 10 mK. We
performed a thorough analysis of these new measurements
together with results obtained during the past five years to find
a potential dependence of the low-frequency excess noise on
the SQUID design and fabrication parameters.
II. SAMPLE SELECTION AND DATA ANALYSIS
Our SQUIDs were fabricated using a Nb-Al-AlOx-Nb
trilayer technology with Josephson junctions defined by the
selective Niobium anodization process [1]. The minimum
linewidth and junction dimensions were nominally 2.5 µm.
For the insulation layer, SiO2 sputtered in an Ar plasma from a
stoichiometric target or SixNy sputtered from a Si target in an
Ar/N2 plasma were used. The resistors were made from Pd
(except for wafer C602 with AuPd resistors). The devices
were not passivated. The bottom Nb was patterned by wet
etch, the top Nb, resistors and insulation layer(s) by lift-off.
The film depositions were done in two sputter systems, our
older “Alcatel” system (SCM440/174 from the French
company CIT-Alcatel) and the newer “FHR” system
(customer-specific cluster system MS100x4-AEO from the
German company FHR).
Our noise study involves single SQUIDs as well as arrays
of SQUIDs in different configurations (series or parallel) [4],
[5]. Provided that all SQUIDs in an array are biased at the
same working point and that there is no correlation between
the noise in the individual SQUIDs, the overall flux noise
density SΦ of a SQUID array scales inversely with the number
N of SQUIDs: SΦ ∝ 1/N. In contrast, the energy resolution ε =
N SΦ /2L does not depend on N (L is the SQUID inductance)
[13]. Therefore, ε in units of Planck’s constant h is a more
appropriate figure of merit than SΦ if one compares the lowfrequency excess noise in SQUIDs of different designs and
configurations. This is plausible if one assumes that the lowfrequency excess flux noise is caused by a large number of
fluctuating magnetic field sources on sub-µm scale rather than
by a global field across the SQUID loop. In this case, the
Paper 3EC01 at ASC2010, to appear in IEEE Trans. Appl. Supercond. 21 (2011)
TABLE I SQUID TYPES USED FOR THE MILLIKELVIN NOISE STUDY
Type
Ref.
N
L/pH
Tmin/mK
Description
C1
C6
C3-C5
C4-C5
C4-C5
C5
C5
C4
C5
C5
C4-C6
C2
C5
We87
Ca98
Me01
Bo09
[3]
—
[4]
[4]
[4]
[5]
[5]
[4]
—
[4]
—
[3]
—
[8]
[15]
[16]
[17]
1
1
1
1
16
16
40
16
14
1
1
1
1
1
1
1
1
30
33
85
115
145
180
60
135
135
20
50
110
120
200
15
80
270
310
16
9-320
10-300
10-320
10
10
9-310
10-300
10
10-16
310
10
90
900
100
53
4pGrad, slotted-washer design
8pGrad, w/o double-transformer
4pGrad, with double-transformer
4pGrad, w/o double-transformer
2sGrad, standard SQUID array
2sGrad, linearized 2stage array a
2sGrad, 2nd stage of 2stage array
2sGrad, 2nd stage of 2stage SQUID
2sGrad, 2nd stage of 2stage SQUID
2sGrad, single current limiter cell
2sGrad, opt. bottom Nb uncovered
2sGrad, SQUID loop in top Nb
2sGrad, similar to 2nd stage cell
Magnetometer with PbIn loop b
12pGrad, multiwasher design
2pGrad, Quantum Design sensor c
2sGrad, thin-film susceptometer
All PTB sensors are designed as gradiometers; the configuration is quoted
in short form, e.g., 4pGrad = 4-loop parallel gradiometer or 2sGrad = 2-loop
series gradiometer. Unless otherwise noted, the SQUID loop is formed by the
bottom Nb and the Nb input/feedback coils are realized on top, separated by a
sputtered SiO2 or SixNy insulation layer. A range for the minimum operation
temperature Tmin is quoted if devices of same type were operated at different
Tmin. For comparison, four devices reported in literature are included in the
study (bottom section of table).
a
Operated without on-chip linearization (output current feedback).
b
Sample C1 in [8]; 10 Hz excess noise at 4.2 K determined from 1 Hz
value using the quoted frequency dependence SΦ ∝ 1/f .
c
Published 100 mK noise spectrum extrapolated from 20 Hz to 10 Hz.
prises four slotted washers with off-washer input coils to
minimize stray capacitance. The bottom Nb in the test
SQUIDs and SQUID arrays is ≈6 µm wide to avoid flux
trapping when cooling the devices in the Earth field [18]. For
the gradiometric 50 pH test SQUIDs, a variant is available
where the SQUID loop is kept free from any covering material
except in the junction region and loop crossing.
We selected the excess noise at 10 Hz as a figure of merit
rather than at 1 Hz [8] because this reduces the measurement
time and the magnetic shielding requirements. Furthermore,
drift effects might become important at low frequencies, e.g.,
caused by slow variations in the operation temperature.
SQUID arrays are more sensitive to such effects than single
SQUIDs because environmental noise and temperature
fluctuations affect all SQUIDs in an array coherently. This
leads to a net effect independent of N, whereas the flux noise
density SΦ scales with 1/N.
The low-frequency excess noise ε1/f was determined by
fitting the measured overall noise with
ε( f ) = εw + ε1/f ( f ) = εw + ε1/f (1Hz) × ( f / Hz)
-α
(1)
and subtracting the resulting white noise level εw from the
measured noise. For simplicity, we use the notation “1/f ” even
if the exponent α differs from 1. For most of our SQUIDs, the
measured noise spectra have not been stored during
characterization, but rather the noise levels at selected
frequencies were read out from the spectrum analyzer display
and listed in the SQUID data sheets (typically at 0.1 Hz to 100
kHz in factor of ten steps). These lists of noise levels were
used to determine the important quantities εw and α. An
example of the achievable fit quality is given in Fig. 1. The fit
curves obtained from six noise levels between 1 Hz and 100
kHz describe the complete spectra very well. At 4.2 K and
high frequencies, ε1/f becomes uncertain due to the relatively
high white noise level.
For our study, measurements were considered when noise
data between at least 10 Hz and 100 kHz were available at mK
temperatures. Only low-noise SQUIDs with ε1/f < 70 h at 10
103
ε / h or ε1/f / h
excess flux noise density SΦ,1/f increases with the number of
contributing field sources (those nearby the Nb lines forming
the SQUID loop), i.e., with the perimeter rather than the area
of the SQUID loop [9]. As the loop inductance is approximately proportional to the perimeter, the ratio SΦ,1/f /L ∝ ε1/f
should remain almost constant. This picture is consistent with
our SQUID noise measurements. Furthermore, we observed
that our multiloop magnetometers with stripline “spokes” [4]
have a higher low-frequency noise than those with coplanar
“spokes” for the same total SQUID inductance [14]. The long
interconnecting striplines pick up a considerable amount of
excess flux noise, but do not contribute significantly to the
total loop inductance. These devices with atypically high lowfrequency noise were not included in the presented study.
Table I describes the selected types of PTB SQUIDs. There
are three basic categories: “regular” sensors used for practical
SQUID applications, second stages of integrated two-stage
sensors, and special test devices intended for noise investigations (from top to bottom). Results from other groups were
also included for comparison (bottom section in Table I). We
regarded SQUIDs fabricated with the Nb-Al-AlOx-Nb trilayer
technology, for which noise spectra at 4.2 K and mK
temperatures were published in the frequency range between
10 Hz and the white noise regime [15]-[17]. In addition, a
SQUID with Nb-NbOx-PbIn junctions and a loop made from
PbIn was considered [8].
There is a large variety of devices, ranging from small
gradiometric 20 pH test SQUIDs with ≈10 µm diameter loops
to double-transformer sensors with 1.05 µH input inductance
covering over 1 mm2 chip area [4]. The PTB C1 device com-
2
T = 4.2 K: α = 0.53, εw = 27.8 h, ε1/f(1Hz) = 70 h
310 mK: α = 0.70, εw = 2.3 h, ε1/f(1Hz) = 490 h
102
4.2 K
101
310 mK
100
10-1
C214G05
L = 110 pH
100
101
102
f / Hz
103
104
105
Fig. 1. Noise spectra of a C2 test SQUID operated at 4.2 K and 310 mK.
Black lines show the total noise ε, gray lines the 1/f component ε1/f obtained
after subtracting the white noise levels which were determined by fitting the
measured noise with (1) at six discrete frequencies between 1 Hz and 100
kHz. Dashed lines show the 1/f components of the fit curves.
Paper 3EC01 at ASC2010, to appear in IEEE Trans. Appl. Supercond. 21 (2011)
C2
C1
C4
C3
C6
C5
1000
f = 10 Hz
ε1/f / h
Hz and 4.2 K were included. The SQUIDs were operated in a
flux-locked loop with the XXF-1 readout electronics [19] and
a single-stage or two-stage configuration [13]. In the case of
single-stage readout (SQUID arrays and a few single
SQUIDs), the preamplifier noise contribution was subtracted.
In contrast, for two-stage setups no correction was required
except for some cases where the second stages degraded the
overall low-frequency noise. Here, the 1/f noise contribution
from the second stage was subtracted. The second stages of
the integrated two-stage devices were measured with the first
stages unbiased. Nyquist noise in the bias resistor caused a
high excess white noise impeding a precise determination of
the 1/f noise contribution at 4.2 K (at mK temperatures there
was typically no problem). All available noise data from the
selected samples were used for the graphs in Section III.
3
100
Bottom Nb anodized
10
2004
2005
2006
2007
2008
2009
2010
Fabrication date
The measurements at 4.2 K were done by immersing the
devices directly into liquid helium. Low-temperature experiments were performed in a 3He cryostat at about 300 mK, in
an adiabatic demagnetization refrigerator around 100 mK, or
in a 3He-4He dilution refrigerator down to 10 mK. Environmental noise was suppressed by a superconducting shield
except in the case of the dilution refrigerator. Therefore,
experiments below 100 mK were restricted to magnetically
very insensitive devices (test SQUIDs and SQUID arrays) and
frequencies above about 10 Hz where the environmental noise
drops below the intrinsic SQUID noise. We are currently
designing a magnetic shield for the dilution refrigerator to
extend our measuring possibilities.
Fig. 2 gives an overview of the low-frequency noise quality
of our process in the past six years. At 4.2 K (open symbols in
Fig. 2), there was no observable dependence of ε1/f on the
SQUID design or fabrication parameters. In contrast, at mK
temperatures (filled symbols) the low-frequency excess noise
was significantly higher when the FHR system was involved
in the SQUID fabrication. There was only one SQUID with
FHR involvement that achieved ε1/f < 80 h at <320 mK and 10
Hz (marked by an arrow in Fig. 2), whereas all SQUIDs without FHR involvement (triangles in Fig. 2) remained below this
limit. Note that the SQUID design, the number of insulation
layers (vertical lines in Fig. 2), the large-area anodization of
the bottom Nb, and the substrate used (cf. Table II) caused no
observable effect on the mK excess noise. Possibly, the
relatively low noise of the C2 devices was related to the fact
that the SQUID loop was realized in the upper Nb layer.
We tested on sample basis that there was no dependence of
the low-frequency excess noise on the SQUID bias point, and
that the noise was not caused by critical current fluctuations
(no improvement by using bias reversal [1]). The lowfrequency noise did not noticeably change between 10 mK and
430 mK. In contrast, the white noise increased slightly at 430
mK compared to 10 mK, consistent with a minimum effective
temperature of the shunt resistors of about 300 mK due to the
hot-electron effect [20].
The influence of the FHR sputter steps is clearly visible in
the distribution of the 10 Hz 1/f noise components (Fig. 3). At
4.2 K, no systematic effect is visible, whereas at <320 mK the
Fig. 2. 10 Hz 1/f noise component at 4.2 K (open symbols) and <320 mK
(filled symbols) plotted versus fabrication date. The denotation of symbols is
given in Table II. The fabrication periods of the sensor versions C1 to C6 are
shown at the top of the diagram. The only sensor with Nb or SiO2 deposition
in the FHR system that remained below the 80 h limit (dashed line) at mK
temperatures is highlighted by a 45° arrow. Vertical lines mark wafers with
two insulation layers on the SQUID loop, horizontal arrows mK measurements of C5 devices without material on the SQUID loop. Large-area anodization of the bottom Nb was used until end of 2007.
TABLE II DENOTATION OF SYMBOLS USED IN FIGS. 2, 4, 5
Symbol
Substrate
Bottom Nb
Insulation layer
○●
Si+SiO2
Si+SiO2
Si+SiO2
FHR
FHR
Alcatel
SiO2 (FHR)
—
SiO2 (FHR)
Si+SiO2
Si+SiO2
Si+Si3N4
Al2O3
Alcatel
Alcatel
Alcatel
Alcatel
SixNy (Alcatel)
□■
◇◆
△▲
▽▼
▷▶
◁◀
—
SixNy (Alcatel)
—
The substrates are 3" wafers, commonly silicon with thermally grown
oxide (Si+SiO2). Alternatively, silicon with silicon nitride cover (Si+Si3N4) or
sapphire (Al2O3) were used.
distributions move to higher excess noise levels with increasing number of FHR sputter steps. Note that for the last C5
wafer we directly checked that the noise degrades with the
number of FHR steps: the 50 pH test SQUIDs without
covering material on the SQUID loop (horizontal arrows in
Fig. 2) showed a substantially lower mK 1/f noise than the
other devices from the same wafer with SiO2 (two FHR steps).
15
NSample
III. RESULTS
0 x FHR
1 x FHR
2 x FHR
(a)
4.2 K
10
(b)
< 320 mK
5
0
10
100
ε1/f (10 Hz) / h
10
100
ε1/f (10 Hz) / h
1000
Fig. 3. Number of measured samples NSample vs. 10 Hz 1/f noise component at
(a) 4.2 K and (b) <320 mK. The number of FHR process steps is illustrated by
the fill color (white: 0×FHR, gray:1×FHR, black: 2×FHR).
Paper 3EC01 at ASC2010, to appear in IEEE Trans. Appl. Supercond. 21 (2011)
1000
The excess noise ratio (ENR) is defined here as the ratio of
the 1/f noise components at mK temperatures and 4.2 K: ENR
= ε1/f (Tmin) / ε1/f (4.2K). We use it to estimate the mK noise
quality of our wafers from SQUID characterization at 4.2 K.
Fig. 5 shows that the measured ENRs were below or above 2.8
(dashed lines) for devices fabricated without or with FHR
sputtering, respectively. A reasonable agreement between our
“all Alcatel” devices and those reported in literature is found.
We could not observe a systematic dependence of the ENR on
the absolute 1/f noise level or the SQUID inductance L. There
is a trend that the low-frequency noise in SQUID arrays (filled
symbols in Fig. 5) is slightly higher than in single SQUIDs
(open symbols), presumably caused by variations of the lowfrequency noise performance along the array. The lower limit
for our currently achievable mK noise is set by a 50 pH test
SQUID of type C6 operated at 16 mK: ε = 0.62 h at 100 kHz,
increasing to 1.64 h at 1 kHz and 14 h at 10 Hz.
f = 10 Hz
Me01
We87
ε1/f / h
100
4
Ca98
10
f = 1kHz
1
IV. DISCUSSION
0.4
0.6
0.8
1.0
α
Fig. 4. 10 Hz (top) and 1 kHz (bottom) 1/f noise components at 4.2 K (open
symbols) and <320 mK (filled symbols) plotted versus exponent α according
to (1). The denotation of symbols is given in Table II, details of literature
devices in Table I. Dashed lines show approximation (2). Arrows help to
relate outlier data points to the corresponding frequency.
The increase in the excess low-frequency noise is accompanied with a rise in the exponent α (see Fig. 4). In semi-log
plot, the dependence may be fitted by straight lines, yielding
the approximation for the 1/f noise in our SQUIDs
ε1/f ≈ 0.09 h × ( f / 200 kHz)
-α
.
(2)
Equation (2) is depicted in Fig. 4 by dashed lines; most of the
data points lie within a factor of 2 around them. The literature
values (stars in Fig. 4) are roughly consistent with our measurements results except for “Me01” [16] with α ≈ 1; possibly,
other low-frequency noise sources were involved here.
100
f = 10 Hz
ENR
(a)
(b)
f = 10 Hz
10
We87
We87
The noise behavior of our SQUIDs at mK temperatures is
generally consistent with the study by Wellstood et al. [8]. For
low-noise devices, similar α values below ≈⅔ were observed.
At 4.2 K, however, Wellstood et al. found “true” 1/f noise
(α ≈ 1) which originated from other sources than the mK noise
and decreased with temperature [21]. This 4.2 K excess noise
is typically not present in our SQUIDs, and α ≈ 0.6 is found at
4.2 K as well. Such weak frequency dependences of the 1/f
noise above ≈1 Hz were also observed in literature [22]-[24].
The ENRs of our SQUIDs were above or below 2.8
depending on whether the bottom Nb or insulation layer were
fabricated in the FHR instead of the Alcatel system. In the
case of the insulation layer, the material involved (SiO2 vs.
SixNy) could be of importance; however, the mK noise level
observed with SiO [15] or SiO2 [17] insulation is comparable
to that of our SQUIDs with SixNy insulation. There are two
main differences between our sputter systems: (1) the Alcatel
system uses a diffusion oil pump with a liquid Nitrogen trap,
whereas the FHR system is equipped with a turbo molecular
pump resulting in a higher water content in the sputter chamber, and (2) the FHR system is dimensioned for substantially
higher deposition rates than the Alcatel system. We are
currently modifying the FHR system to obtain lower
deposition rates. Further noise investigations are planned. Our
hope is to find the reason for the increase in the low-frequency
noise caused by the FHR system, and to learn from that how to
modify the fabrication process for minimum noise at mK
temperatures.
Me01
Bo09
Me01
ACKNOWLEDGMENT
Bo09
1
Ca98
Ca98
10
100
ε1/f (4.2 K) / h
10
100
L / pH
Fig. 5. 10 Hz ENR plotted versus (a) 10 Hz 1/f noise component at 4.2 K and
(b) SQUID inductance L. The denotation of symbols is given in Table II,
details of literature devices in Table I. Open symbols mark single SQUIDs (N
= 1), filled symbols series SQUID arrays (N = 14 or N = 16). Dashed lines at
ENR = 2.8 separate devices without and with FHR sputtering.
The authors thank Cornelia Aßmann, Marianne Fleischer,
Alexander Kirste and Frank Ruede for SQUID characterization at 4.2 K, Marcel Scheuerlein and Franz Müller for fabrication of wafer C602, and Marco Schmidt for operation of the
dilution refrigerator. The low-temperature noise measurements
of sensor C509U33A were performed at the University of
Zaragoza by María José Martínez-Pérez, and those of C423F33A at the University of Heidelberg by Jan-Patrick Porst.
Paper 3EC01 at ASC2010, to appear in IEEE Trans. Appl. Supercond. 21 (2011)
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