Development of SFQ Multi-Chip Modules for Quantum Bits

Abstract

We developed a multi-chip module (MCM) system of superconducting quantum bits with single-flux quantum (SFQ) interface circuits. The MCM system consists of chips with quantum bits and chips with SFQ circuits mounted on a base chip by flip-chip bonding (FCB) with superconducting solder. We report on a reliability test of the MCM system. The test was done using a resistance measurement of an MCM with 30 mum diameter bumps. Tested samples showed good durability against thermal cycles between room temperature and 4.2 K. At 4.2 K, the resistance measured through more than two hundred bumps in a series was less than 1 mOmega. Along with achieving a high reliability, reducing thermal interference from SFQ circuits to quantum bits is important. We must understand the thermal conductance between and within the chips to design a system with minimum interference. An MCM on-chip thermometer which is based on the Johnson noise thermometry, has been designed and fabricated to achieve this desired level. The preliminary results of the thermal measurement are reported.

Full text

158 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 17, NO. 2, JUNE 2007
Development of SFQ Multi-Chip Modules for
Quantum Bits
Toshiyuki Miyazaki, Shinichi Yorozu, Masaaki Maezawa, Mutsuo Hidaka, and Jaw-Shen Tsai
Abstract—We developed a multi-chip module (MCM) system
of superconducting quantum bits with single-flux quantum
(SFQ) interface circuits. The MCM system consists of chips with
quantum bits and chips with SFQ circuits mounted on a base
chip by flip-chip bonding (FCB) with superconducting solder.
We report on a reliability test of the MCM system. The test was
done using a resistance measurement of an MCM with 30
diameter bumps. Tested samples showed good durability against
thermal cycles between room temperature and 4.2 K. At 4.2 K, the
resistance measured through more than two hundred bumps in a
series was less than 1 . Along with achieving a high reliability,
reducing thermal interference from SFQ circuits to quantum
bits is important. We must understand the thermal conductance
between and within the chips to design a system with minimum
interference. An MCM on-chip thermometer which is based on
the Johnson noise thermometry, has been designed and fabricated
to achieve this desired level. The preliminary results of the thermal
measurement are reported.
Index Terms—DC SQUID, quantum bits, SFQ, thermal conduc-
tance.
I. INTRODUCTION
SUPERCONDUCTING quantum bits consisting of
Josephson junctions are a promising candidate for creating
a quantum computer. However, a superconducting quantum
bit requires a temperature below 100 mK for proper func-
tion and microwave signals for manipulation. The necessity
of microwave lines, which increase the heat load on the re-
frigerator, makes it difficult to create a large format array of
superconducting quantum bits. Thus, cryogenic electronics
that function below 1 K, operate fast and dissipate very little
power are required to create a quantum computer based on
superconducting quantum bits. A single-flux-quantum (SFQ)
[1] circuit, which also utilizes Josephson junctions dissipates
relatively little power and functions very fast (more than 10
GHz) at a cryogenic temperature, is the natural candidate for
the interface between superconducting quantum bits and room
temperature electronics.
Manuscript received August 27, 2006.
T. Miyazaki is with the Japan Science and Technology Agency, SRL, NEC
Tsukuba Lab, 34 Miyukigaoka, Tsukuba, Ibaraki 305-8501, Japan (e-mail:
t-miyazaki@istec.or.jp).
S. Yorozu and J.-S. Tsai are with NEC Corp., 34 Miyukigaoka,
Tsukuba, Ibaraki 305-8501, Japan (e-mail: yorozu@frl.cl.nec.co.jp;
tsai@frl.cl.nec.co.jp).
M. Maezawa is with Advanced Industrial Science and Technology, Tsukuba,
Ibaraki 305-8561, Japan (e-mail: masaaki.maezawa@aist.go.jp).
M. Hidaka is with the International Superconductivity Technology Center,
Tsukuba, Ibaraki 305-8501, Japan (e-mail: hidaka@istec.or.jp).
Digital Object Identifier 10.1109/TASC.2007.898702
Even though an SFQ circuit dissipates very little power,
it is still hotter than superconducting quantum bits [2]. The
thermal properties of a crystal are described by Debye’s law
at a cryogenic temperature, . According to the law, the heat
capacity of a silicon substrate is proportional to , and the
thermal conductance obeys a similar rule. Consequently, the
heat capacity and thermal conductance of a silicon substrate at
100 mK are less than of those at 4.2 K. As a result, the
circuit temperature is easily increased by a very small power
dissipation, and the heat is difficult to eliminate because of the
poor thermal conductance. Although an SFQ circuit is relatively
insensitive to the change in temperature, the thermal noise and
the electrical noise of the circuit caused by the temperature
rise will significantly affect the performance of quantum bits.
A multi-chip module (MCM) scheme has been proposed as a
countermeasure for the thermal interference.
An MCM system consists of many silicon substrates. Mod-
ules are the substrates on which quantum bits or SFQ circuits are
fabricated. Each module is fabricated separately and mounted
using flip-chip bonding (FCB) on to the base substrate on which
the superconducting wiring is fabricated. Because of the lim-
ited contact area and the poor thermal conductance of the super-
conducting bumps, the thermal conductance between circuits of
this design is less than that of a monolithic design. Furthermore,
each module can be cooled separately using the cold finger ap-
proach or by chip-scale refrigerators [3]. This module-based
approach significantly increases the flexibility of the thermal
design and enhances the flexibility of the circuit design of the
system.
We need to study thermal properties as well as the reliability
of the FCB to create an MCM system with SFQ circuits and
quantum-bits. In this paper, we report the reliability experiments
of our FCB process and the preliminary results of a thermal
conductance study.
II. RELIABILITY OF FCB
Low melting point (117 ) InSn solder is used to form bumps
so that the FCB process does not affect the critical current den-
sity of Josephson junctions. Transmissions of SFQ pulses [5] up
to 60 Gbps through 50 diameter bumps and pulses beyond
100 Gbps through 30 diameter bumps have been demon-
strated [6], [7]. These higher speed pulses are sufficient for ap-
plications with quantum bits.
To develop and study the FCB process, we fabricated two
chips with only bumps and superconducting wiring. One chip,
shown in Fig. 1 as “Chip”, is 5 mm square, and the other is
an 8 mm square chip shown in the figure as “Base”, is 8 mm
square. Each chip has 30 diameter bumps and supercon-
ducting wiring (Fig. 2). The circuit contains 264 bumps on all
1051-8223/$25.00 © 2007 IEEE

MIYAZAKI et al.: DEVELOPMENT OF SFQ MULTI-CHIP MODULES FOR QUANTUM BITS 159
Fig. 1. Pair of MCM test chips.
Fig. 2. Schematic of electrical path to test electrical connectivity of bumps.
the sides of the chips and has an opening at one of the corners.
Bumps were spaced adequately so as to avoid a short circuit, and
they were designed to form an electrical circuit with supercon-
ducting wiring. The circuit was designed so that it does not show
electrical conductivity even if a pair of bumps fails to connect.
Other than the bumps with wiring, four hundred bumps were
fabricated to reinforce the mechanical strength of the FCB.
The electrical connectivity was tested using five pairs of
chips. Just after the FCB process was done, all pairs showed
good connectivity at room temperature (the typical resistance
is approximately 700 ). The resistance of all pairs measured
with a resistance bridge at 4.2 K is less than 1 , which
is beyond the sensitivity of the bridge. The superconducting
transition temperature of InSn is approximately 6 K, and the
measured temperature dependence of the resistance strongly
suggests that the bumps are superconducting. The durability
against the thermal cycles was tested with a pair of chips that
survived more than 12 thermal cycles from room temperature
to 4.2 K. Throughout the durability test, the electrical resistance
of the sample at 4.2 K was always less than 1 . Furthermore,
no change in the connectivity was found in all the pairs one
year after the FCB process.
III. THERMAL CONDUCTANCE OF MCM
We must understand the thermal properties of the MCM
system to achieve a good thermal design [2]. On-chip ther-
mometers with good sensitivity and low power dissipation
are indispensable for evaluating thermal properties. The ther-
mometer should also be fabricated with the same process used
for SFQ circuits. We therefore chose Johnson noise thermom-
etry with a dc SQUID to satisfy these requirements.
A. Johnson Noise Thermometry
Johnson noise thermometry is a method to measure the tem-
perature from the thermal noise of an electrical resistor. The
power spectral density of the Johnson noise current of a resistor,
, placed at the temperature, ,is
(1)
where is Boltzmann’s constant. At the cryogenic temper-
ature, the noise current is too small to produce good statis-
tics with a short measurement period. Therefore we utilized a
dc SQUID to amplify the noise current. Because the resistor
does not dissipate power, the temperature should be measured
without affecting the object. Another advantage is that all com-
ponents required by this thermometry can be fabricated with
the same process as the one used for an SFQ circuit. In addi-
tion, a good magnetic shielding is required for the dc SQUID
to operate properly. However, this is not a serious problem with
SFQ circuits or quantum bits, which also require good magnetic
shielding.
From (1), the noise temperature, , of a dc SQUID with
input current noise, , can be described as
(2)
According to [8], the error of the measured temperature
under the condition is
(3)
where is the input inductance of the dc SQUID, and
is the measurement time.
B. Design of dc SQUID
The thermometer resistance and the SQUID input noise limit
the sensitivity of the Johnson noise thermometry. Our goal for
the thermometry was to measure the temperature as low as 10
mK. In our case, the smallest resistance reproducible with real-
istic precision was approximately 5 . After comparing these
values with (2), we determined that the SQUID input noise cur-
rent has to be less than 10 . To achieve this perfor-
mance, we used an array SQUID with multi-turn input coil [9].
The SQUID was designed for NEC’s standard Nb process
[10] and has a critical current density of 2.5 . All resis-
tors in the circuit were made of PdAu instead of Mo in the stan-
dard process so that the circuit can be operated properly below
1 K. The junction of the SQUID is 0.9 square, and its crit-
ical current was designed to be 20 . The inductance of each
SQUID washer was designed to be 50 pH. A four-turn input
coil and a one-turn feedback coil were coupled to each SQUID
washer and the mutual inductance between the input coil and
the SQUID washer was estimated to be 200 pH. 64 dc SQUIDs
were connected in a series to form an array.

160 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 17, NO. 2, JUNE 2007
Fig. 3. Schematic of MCM to measure thermal conductance.
C. MCM Design for Thermometry
Fig. 3 shows the schematic of the MCM we used to measure
the thermal conductance. This MCM consists of two chips. The
first one, which is called “Chip,”is a 2.5 mm square substrate
and has a 5 resistor for the thermometry and a 1 resistor
as a heater. The other one, which is called “Base,”is a 5 mm
square substrate and has a 5 resistor for the thermometry
and two SQUIDs to amplify the noise of the resistors. The actual
layouts of both chips are shown as Fig. 7.
The “Chip”and “Base”were mounted using FCB via 120 50
diameter bumps, and the pair was cooled from the backside
of the “Base”. In this configuration, the “Chip”has no thermal
paths other than bumps for heat to come in or out. The thermal
conductance between chips can be measured precisely by ap-
plying a small current to the heater of the “Chip”while mea-
suring the temperature of both chips.
IV. MEASUREMENT
A. dc SQUID Performances
The electrical properties of the dc SQUIDs were measured at
4.2 K. The critical current of an SQUID array is approximately
18 , and the mutual inductance between the input coil and the
SQUID was found to be 141 pH from the -V characteristics.
The SQUID operates in a flux-locked loop (FLL) to compen-
sate for the fluctuation in the sensitivity due to the change of the
magnetic field. The bandwidth of the FLL, with its handmade
feedback circuit, is a few hundred kHz. It is limited by the room
temperature electronics, and the SQUID input noise current is
less than 20 . This corresponds to a noise temper-
ature of with a 5 resistor.
B. One-Chip Temperature Measurement
To demonstrate the temperature measuring ability, we cooled
the “Base”chip with a cryostat of Oxford Instruments (He-
lioxVL). A SQUID and a 5 resistor were connected on the
chip using an Al bonding wire (Fig. 4).
Fig. 5 shows the noise spectra obtained at various sample
stage temperatures for the cryostat measured by a built-in ther-
mometer. During this measurement, the FLL bandwidth was
limited to approximately 10 kHz due to the poor performance
of the room temperature electronics. Peaks found below 1 kHz
of each spectrum are originated from the electricity supply lines
and a peak at 10 kHz came from the FLL instability. No peaks
Fig. 4. Setup for one-chip temperature measurement.
Fig. 5. Noise spectra of a 5 resistor at various temperatures. The cutoff
frequency was determined by FLL electronics.
Fig. 6. Noise spectral density averaged by frequency vs. temperature. Solid line
is the theoretical calculation including the normal resistance of an Al bonding
wire above 1 K.
and structures were found between 1 to 2 kHz, and the spec-
tral densities of this frequency region were averaged and com-
pared with the sample stage temperature. Points of Fig. 6 show
the comparisons between the averaged noise spectral densities
and the sample stage temperature. The solid line of the plot

MIYAZAKI et al.: DEVELOPMENT OF SFQ MULTI-CHIP MODULES FOR QUANTUM BITS 161
Fig. 7. “Chip”(left) and “Base”of MCM system for thermal conductance mea-
surement.
represents the theoretical prediction of the noise spectral den-
sity, which includes the effect of the normal resistance of the Al
bonding wire above 1 K.
Although the sample stage temperature and the noise spec-
tral density show good agreement with the theory above 2 K,
the measured value at 0.35 K has some discrepancy with the
calculation. The reason for this discrepancy can be explained
by the fact that the sample, which had been glued on by var-
nish, fell off during the cool down and was only supported by
Al bonding wires. Because the chip is only cooled through the
Al bonding wire, the cooling was significantly decreased below
1 K at which point, Al begins superconducting.
C. MCM Measurement
An MCM sample to measure the thermal conductance was
made from the “Chip”and a “Base”pair (shown in Fig. 7) with
the FCB. This sample was installed in a cryostat. But be-
cause of the thermal leakage between the magnetic shielding
of the sample holder and the thermal shielding of the cryostat,
we could not cool the sample below 4.2 K during the measure-
ment period. Also cross talk was observed between the heater
line and the input coils of the SQUIDs. This cross talk signifi-
cantly degraded the accuracy of the measured temperature from
the theoretical prediction by (3). The origin of this effect is sus-
pected to be the common grounding problem in the MCM. Fur-
thermore, no reliable information regarding the “Base”temper-
ature during the measurement was obtained because of a wiring
problem with one of the SQUIDs.
Fig. 8 shows the relationship between the applied power and
the temperature rise of the “Chip”from the base temperature
(4.3 K). From the measurement, we estimated the thermal con-
ductance between the “Chip”and the sample stage to be ap-
proximately 700 . The thermal conductance through the
bumps is close to this value assuming the thermal conductance
between the “Base”and the sample stage is greater than that be-
tween the “Chip”and the “Base”.
V. S UMMARY
Aflip-chip bonding process using InSn solder was developed.
We described a demonstration of the reliability of the process
that was conducted using a chip with an electrical circuit in-
cluding more than 200 bumps. The quality of the connections
did not show any deterioration after thermal cycles and being
Fig. 8. Temperature rise vs. applied power of the “Chip”. During the measure-
ment, the sample stage temperature was 4.3 K.
kept in a room temperature environment over a period of more
than one year.
An on-chip thermometer that was fabricated using a standard
process for SFQ circuits and based on the Johnson noise ther-
mometry was also developed. Although demonstrations showed
that it could measure the temperature, there is room for im-
provement when measuring the thermal properties of an MCM
system. The maximum SFQ circuit scale allowable has to be
determined using more precise thermal properties of the MCM
system and the cooling power of a refrigerator.
ACKNOWLEDGMENT
The authors would like to Michiyo Isaka for her help in fab-
ricating the chips.
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